AVCO PlasmaRadiationShield 1967

THE PLASMA RADIATION

NASA CONTRACTOR REPORT

I

CO

_D

<

O

< Z

CONCEPT,

NASA-GEORGE

GPO PRICE

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Prepared

Richard

CFSTI

AVCO

copy

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For

H.

.July

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ff

TO

SHIELD:

AND APPLICATIONS

MARSHALL

Huntsville,

ALabama

FLIGHT

Contract

8-20310

SPACE

Francis

French

OR AD NUMBER)

NAS

CR OR TMX

(ACCESSION

No.

and

W.

NUMBER)

(PAGES)

by

C.

(NASA

X

— J

—

i.

under

Levy

CORPORATION

$

$

(HC)

(MF)

NASA

October

9, 1967

CR-61176

CENTER

(CATEGORY)

(CODE)

{THRU)

/

SPACE VEHICLES

October 9, 1967

CONCEPT,

VEHICLES

by

W.

By

No.

AND

THE

NAS

under

AVCO

8-20310

Contract

Prepared

Report

French

PLASMA

Richard

SHIELD:

EVERETT

H. Levy

RESEARCH

TO SPACE

RADIATION

(Contractor

and Francis

Dated April

APPLICATIONS

C. MARSHALL

CORPORATION

LABORATORY

Responsibility

Massachusetts

• GEORGE

organization

a division

Laboratory

exchange.

FLIGHT

provided

Sciences

prepared

Everett,

SPACE

in the

AVCO

author

Space

report

that

this

For

the

the

for

of

of

or

in

is

NASA

CR-61176

of

it.

interest

contents

NASA

CENTER

Distribution

information

resides

that the concept

but important

using

of Plasma

The

to do with

and

Plasma

and magnetic

solar

is reviewed

remain

of the extremely

into a realistic

and

The

control

electric

energetic

questions

indicates

Shielding

the concept

The

have

high

NOT

space

these

sound,

areas:

fields

Shield

device

vehicle

design.

concept

voltages

studies.

protons.

ABSTRACT

required,

Radiation

FILterED.

of shielding

PRECEDING

is an active

is physically

flare-produced

PAGE BLAI_:(

for the purpose

in at least two

in the light of current

-iii-

of

from

with

free

evidence

Radiation

available

practical

electrons,

astronauts

integration

establishment

CONCEPT

RADIATION

.

.

.

°

o

.

.

.

SUPERCONDUCTING

OF

THE

l_O’r

SPACE

11.

TABLE

Abstract

PLASMA

PLASMA

IN THE

PREFACE

CONTENTS

SHIELDING

SHIELDING

SELECTION

RADIATION

RADIATION

RESTRICTIONS

CONFIGURATION

VOLTAGE SHIELD

PRECrr.DING PAG6 BLANK.

CONSIDERATIONS

REQUIREMENTS

LEDGMENTS

SYSTEMS

SYSTEM

COIL

-V-

CONCLUSIONS

VACUUM

APPENDIX

ACKNOW

OTHER

REFERENCES

35

iii

59

75

73

finished,

a

it

if

is

to

be

on

far

To

the

that

The

text,

with

such

from

dealt

prove

Shield

device

present

profile.

radiation

However,

astronauts

worthwhile

comparatively

Radiation

summary

shielding

conclude

Plasma

weight

brief

This

very

The

and

To

To

To

Plasma

long

follows

that

is

Research

to

if

consider

explain

concept;

outline

concept,

resolved;

extract

to arise

realistic

discuss

where

tially

organization

summary

that

a

it

it

is

is

is

is

in

to

in

to

in

to

of

of

of

be

an

be

on

by

I.

the

the

the

the

the

the

the

the

not

has

any

that

low

that

The

cost

way

with

deep

solar

from

large

paper

space

offers

active

useful

flares.

nature

means

Shield

device

results

certain

certain

aspects

Plasma

yielded

broader

broader

concept

prospect

practical

intended

missions

provided

Shielding

Radiation

Radiation

PREFACE

successful,

compatible

accomplish

encouraging

in weight,

a preliminary

of the Plasma

the fundamentals

a list of possible

in integrating

the present

of research

the Plasma

particular

the above

Radiation

electrostatic

emphasis

preliminary

discussions

desirability

promising.

spacecraft

advanced

shielding

methods.

thorough

status

a more

radiation

possible.

schemes

problem

follows:

systems

general

finding

discuss

design;

viewed

neither

Shield

nature

points

with

from

These

space

paper

looks

these

these

areas

only

this

and

We

the

the

the

the

are

as

of

of

of

of

of

as

in

to

to

is

intended

penetrating

the

it will

radiation

principle,

features

space

point

problems

sense.

following

Radiation

problem

Shield

terms,

type

In Section

shielding

unconventional

magnetic

concept

it

at

to

of

In

be

the

this

that

that

con-

must

seems

proton

protect

Plasma

mission

although

shielding

Radiation

aspects

objectives:

successful.

Shielding

still to be

quantitatively

shielding,

of the

likely

problem.

areas

2 we

leaves

essen-

study.

with

being

light

This

give

still

the

the

as

in

a

a

on basic

on the uncertainties

are thoroughly

in the Plasma

size is determined

compatibility

million

8. take

Radiation

restrictions

requirements,

Radiation

and that studies

appendix

concept.

remains

is likely to be of interest.

principles

are

determination

vehicle.

the superconducting

principally

problems

definitely

of research

in spite of favorable

of the Plasma

The

are

are

such

depth

these

other

merits

study;

Shield

greater

concept

subject

running;

problems

problems

Radiation

vehicles.

discussed

the basic

particular

in Section

of Section

that these

to a space

the present

miscellaneous

configuration,

straightforward

difficult practical

status

again,

done.

Here

An

We

The

and

The

and

The

our

with

have

are,

from

size,

These

30-60

Shield

design

Shield

firmer

before

appear

coils,

factors

Section

is more

that we

conclude

required

sections

9 offers

the size

Radiation

succeeded

following

Radiation

problems.

(5 through

parameters

two basic

associated

the Plasma

the vacuum

the Plasma

conclusions

conclusions

in adapting

complicated,

as the crew

in isolating

the voltage.

respectively,

of importance

of the Plasma

of the voltage

on the physics

that the range

can be reached.

difficult but not insuperable,

of the underlying

initial results,

much

work

-2-

by

in

up

the

the

and

and

with

from

about

volts

launch

Shield

is the

on the

Shield,

the most

discusses

to be

radiation

considered ..._

The

because

mission.

as to the protons

belts.

that cause

it is apparent

doses

are

it.

with

doses

space

erally

Manned

extended

missions

radiation

altitudes

the crew,

environment,

interplanetary

occurring the

easily neutron

the degree

agreement

radiation

demanding

There

restrict

data

future

_This

ideal,

large

solar

will

but,

We

can

are

be

so

is

a

field on lunar

of the unattenuated

components

received

(e. g.,

components

edges

can

to limit

of the large

subjected

{in extreme

and

are

and

must

Since

flare

solar

flare

space

SPACE

hazard

levels.

effects

because

outside

to much

at high

be made

Vehicles

missions

illness,

orbiting

vehicles

the more

the same

SHIELDING

and even

radiation

electrons

radiation

important

principal

subjected

RADIATION

is a wide

the earth

the solar

protection

inadequate

associated

discomfort,

radiations,

Of the two

environment.

the galactic

of the doses

environmental

to acceptable

is compounded

to the hazards

with the outer

that provisions

the geomagnetic

of the integrated

the (principally

one spectrum

to astronauts

hand, space.

the present

environment

in opinion

other in

radiation

variation

by solar

factors.

quantitative

considering

appreciable

impossible.

acceptable.

Astronauts

essentially

flares.

radiation;

to two

shielding

particles.

First,

(e.g.,

accident,

radiation

radiation

probably

energies

because

galactic

Refs.

posed

against

hazard

terms,

flares,

only

been

hand,

order

them

there

solar

has

with

case

and,

that

live

this

the

On

the

the

the

the

for

-3-

on

no

an

of

of

to

in

to

is

is

is

I to 29) concerning

to

the

and

over

death

cases)

result

fluxes

is gen-

of this

on long

as well

duration

associated

the latter

in absorbed

synchronous)

of the trapped

the anticipated

portion far

quantitative

foreseeable

component

through

purposes,

naturally

radiation

galactic

This

lack

more

of is

one

UV)

due

not

the

the

of

of

to

is

adequate

obtained

dangerous

the

of magnitude

practical

in

situation

ourselves

charged electromagnetic

screened;

radiation

fortunate

considered

than

have

in

of hazard

can be attributed

on the space

solar cycle.

shielding material and alpha particles,

dose criterion

flare.

If it

This data suggests that

to make a use-

ful art out of forecasting the occurrence of major

wide range in intensity of different

Further,

to predict

confidence levels appropriate to the more intense flares. of radiation conditions to be encountered on future flights based on this

Thus, postulation

modest experience is questionable.

on the response

of the human body to the type of radiations encountered in space is limited. This deficiency is due to the lack of experience with a natural source of

protons on earth, difficulties

in simulating the fluxes of high energy par-

ticles in the laboratory, use of human subjects for hazardous experiments.

considerations which preclude the

The simplest method of providing radiation protection is to use bulk

to stop the incident

flare protons the most appropriate materials have low atomic num-

radiations.

bers (e.g., water, polyethylene).

long-duration missions,

of shielding required can be reduced if body is taken into consideration. involved in formulating

the recovery capacity of the human

there are many uncertainties

on this basis, 27, 30

and the shielding requirements,

while reduced, are still substantial.

example, Martian mission are given in Ref. 27 to be 17 gm/cm Z using a cumulative

the amounts of polyethylene shielding required on a two-year

and 7 gm/cm using a criterion

takes into account

biological been suggested, 26’ 31 depending on the desired probability

recovery.

figures have recently of not exceeding

some stated dose and the phase of the solar cycle. Some of these figures are given in Table 2. 1.

is desired to co_npletely shield a cylindrical

vehicle 15 ft

(-_4. 6 m) in diameter by 25 ft (_7. 6 m) long with 7 gm/cm 2 of material,

shielding material would ,veigh about 22,000 lbs (_10,000

kg). An alternate

procedure to shielding, _he entire vehicle is to shield only a minimum-size storm cellar

to which the crew can retire in the event of severe solar

This approach, however,

probably rules out normal

of the crew and

the duration of the

This restriction

compromising to the success

For

flares.

Second,

For solar

information

and humanistic

it will be very difficult

flares makes it difficult

However, a radiation tolerance criterion

On the other hand, much larger

could be particularly

flight and scientific

severely restricts

the activities

duties for

that

-4-

the

the

the amount

As an

flares.

the

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we

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a whole,

presently

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stantially

2. I Pure

is clearly

the hazard

the degree

of the mission

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by the geomagnetic

sible to achieve

for a particle

is desired

the scene

the earth

magnetic

as pure

protons

cut-off

(known

either

It has

these

occur

sign.

flare

which

MeV;

long

note

enon

been

We

been

into a brief

in radiation

To

us

and

with

This

known

flare

then,

flare

phase

_eight

survey

during

occurs

schemes

protons

schemes

to draw

launches

afforded

whether,

is “Pure

be acted

shielding

shielding

radiation

Shieldin_

particles

radiation

a cruciaL

shielding.

conclusion

worthwhile

the normal

conclusion:

functioning

by a given

to consider

is a system

(and alphas)

of protection

of the space

the kn_wledge

the following

not interfere

can therefore

the shielding

first of these

light in weight.

that will provide

that the spectrum

that will ulti_;ately

the top of the atmosphere

effect of this type

valid for charged

flights so far.

that the method

the equatorial

an appropriate

of geomagnetic

in this sense

in the energy

“Equatorial”

at certain

is equally

of trapped

equatorial

shielding)

for space

S. manned

at either

a certain

of cosmic

particles

electrons

latitude.

particles

are able

to cross

magnetic

magnetic

equator.

function

without

regions

regions

studied

promise

against

energy;

a good

field.

hand,

means

These

range

their

space

near

pole

been

with

-0-

are

has

has

in the form

of all U.

a protective

by carrying

magnetic

first that the method

It appears

to shield

to arrive

field line; on the other

45 ° of the geomagnetic

charged

The

measured

is a strong

is due to the fact that charged

of the space-

of

as

have

review

problem

or solar

constitute

Shielding.”

uncertainty

by electro-

a low-energy

a quantity

therefore,

protected

far from

a single

possible

phenom-

33-42

say,

when

pos-

in

of

of

it

which

upon

Magnetic

rays

exhibits

This

crossing

strongly

within,

have,

It is clearly

vehicles

deal.

particles

43,44

up to several

locations

field lines that increase

it is clearly

field coil; this possibility

particularly

for which it

The Radiation

arrangement

machines.

meaning

voltages

voltages

sound.

ductor

There

detail

attain

other

Pure

two

this

2.2

the

the

of

In

at

the geomagnetic field, but are essentially

unknown in deep space. Magnetic

radiation shielding of the type in which the field extends to “infinity”

attractive

since the radiation hazard caused

by the electrons is not due so much to the penetration of the primary trons, as to the comparatively

long range of the secondary x-rays and

-rays produced by stopping the electrons.

These secondaries are absent

in the magnetic radiation shield.

Whereas pure magnetic radiation shielding against

looks attractive

the same cannot be said of using pure magnetic

radiation shielding against solar

flare protons in deep space. The reasons

this situation are strictly

is desired to shield have higher

flare protons against

than the trapped elec

trons, and therefore require more intense magnetic fields to do the job.

The situation has been studied both roughly and carefully;

is always that except for cases where it

is desired to stop very energetic

(_ I BeV) protons from penetrating into large volumes,

tage of pure magnetic shielding over solid shielding is not great enough to

compensate for

plexity of the active system. definitive.

This conclusion can probably be regarded as

and increased com-

today,

rigidities

the solar

quantitative;

the substantially

reduced reliability

in this application

space

massiveness

electrostatic

conductors

connection

considered

machines,

“infinity.”

20 MV,

technical;

explained

Shieldin_

a whole

potential

between

Without

pictured

scheme,

charged

relative

scheme

vehicle

vehicle

vehicle

speaks

shells,

which

found

forms

shells

itself.

detail

space

space

these

these

earth

with

high

pure

first

two

this

the

the

the

the

are

are

for

-7-

act

on

as

as

of

as

as

of

of

to

in

in

to

is

is

is

is

is

It

a

electrically

the weight advan-

is

elec

the conclusion

trapped electrons

de Graaff

constructed

capacitor.

in Van

virtually

charged

neutral.

Plasma

neither

certain

cannot

largest

steady

going

being

great

with

con-

into

and

the

as

In

In

is

a

Electrostatic

one

concentric

arrangement,

some

difficulty

produced

The

Shield.

the

is

nevertheless

shielding,

as

space

to do the

slightly

high

system

charges

would

time.

The

that the

neither

attractive;

of a sufficiently

conclusions

situation

scheme

“Plasma

of this paper

any

and

The

nor

From

same

true

pure

trons

weigh

would

scheme

charge

system

vehicle

protons

becomes

in deep

It might

magnetic

obvious.

positive

however,

in space

shielding

the case,

prevailing

to respond

particularly

furthermore,

that the insulators

the field of “active”

substantially

fundamental

Shielding”

this type

Radiation

to which

which

now

we

that would

job.

difficulty

be thought

space

electrons

to an electric

substantial

if (as is always

as a protection

would

quite

the foregoing

electrostatic

the limitations

character

modified

has been

turn

and

sign

wind

good

than

with

short

These

since

would

these

looks

10/cc.

scheme

against

methods

on both

opinion)

protons.

required

of about

so short

far more

energetic

shielding

radiation

discharge

potential

of either

in a time

in a very

the case)

the solar

one tried

considered

insulator.

the second

it is clear

to maintain

be required

unrealistic.

to a density

that (in our

is, perhaps,

the potential

that the very

that it is very

itself be a very

the solid material

fills the planetary

by an electrostatic

in the first instance

field of the type here

is the so-called

is the principal

by technological

our attention.

developments.

put forward.

to the only

radiation

shielding

that our

unlikely

subject

scheme

other

which

This

open

This

-8-

are

is

are

pure

free

This

dis-

free

free

with

This

less

elec-

could

vacuum

is not

shielding

the space

leaves

and

be

of

Radiation

Plasma

fields,

field is the direct

the shielding

protons,

ing the electric

Radiation

shield.

of 30-100

the achievement

and

The

magnetic

energetic

the order

the Plasma

3. I Plasma

the electric

electrostatic

is a surprising

of the Plasma

of the Plasma

as a single

arrangement

statics.

positive

reasons)

voltages

liminary

voltages

special

current

vehicle

while

with

Now,

good

are

3.2

We

We

status

until positively

charge

CONCEPT

the use

fields are

as that required

the establishment

purpose

field that is required

We

MV,

THE

been

ever

i.e.,

while

means

higher

Shield

field.

PLASMA

require

of such

voltages

purposes

involves

the sole

than has

SHIELDING

therefore

Radiation

Shielding

RADIATION

field has

It follows

of the two

of providing

Shield 46’47

the magnetic

demonstrated,

but the specific

is just the same

that the electric

first the electrostatic

fact that the concept

(] on its surface;

in an integrated

of this section,

on the problems

of the Plasma

first subject

to infinity.”

of terminals.

will present

of a voltage

the electric

a conducting

Shield. The

that follow

is radially

of research

or induced

of various

introduced

associated

electrical

engineers

virtually

Shielding

the very

of other

consider

charges)

sections

vehicle.

concept.

we hope

to show

of deep

between

reasons

aspects

meaning

between

sphere

space

there

sound

space

pairs

must

-9-

are

Now

any

we

An

to considering

Radiation

Radiation

achieved

to hope

on

for

remain

against

of both

electric

in doubt

on earth.

that under

of support-

as follows:

of a voltage

for the pure

of a space

that such

the basic

the basic

describes

in terms

of this,

electro-

carrying

features

by this

to pre-

physics

of the

Shield

viewed

used

from

{for

are

the

and

the

the

it

a

a

outwards

In view

a conductor

_n elementary

of radius

field produced

are devoted

Radiation

appendix

with

of “potential

in general

device

obviously

in this paper

(in the absence

discussion

system

Electrostatics

consider

respect

applied

conditions

in fact attainable.

In the remainder

infinity is normally

generally

sphere.

47rEorZ

potential

assumed

sphere

is

a)

of

we

the

the

the

the

r(>

case

that

have

E -

terms

above

surface

follows

relevant

potential

In defining

Comparing

necessary

electron

exceeds

isolated

sphere.

on an

charges

related

energy

sphere

sphere

sphere

bring

value

volts.

have

this

For

our

just

the

the

the

the

the

the

by

to

is

is

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to

quantity

is

is

at

at

of

of

of

as

=

be

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an

Q

Q

(of

the

can

and

this

this

The

that

may

field

(a)

from

from

4_£0r

radial

space.

distant

Shield

Plasma

always

electric

derived

distance

constant

follows:

A way

_ = 0

a barge

a proton

arbitrary

magnitude

Radiation

interpreting

a potential

O 4_EOa

C — 4_E 0 a

charge eQ

capacitance

capacitance

magnitude)

two-me_er

50 MeV,

(2) we

shielded

infinity;

formula

electron

electron

protons

exclude

= C_

protons

up to

infinity

having

kinetic

proton

energy

energy

against

charge

proton

proton

radius

reach

equal

space

when

volts.

Thus,

4_E0

from

e_(a)

e_(a)

C ,

volts

only

-10o

that

able

this

will

and

and

are

+e)

the

the

the

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see

be

In

to

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to

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in

at

Q

=

a

a

a

.

electrostatically

If we wish

kinetic

Measuring

5 x

capacitor

formula

with

is

field

a

added;

the

this

the

the

source

only

the

we

less

_(a)

the

isolated

It

at

in

in

of

this

work

radius

sphere.

surface

potential

statement

(3.2.1)

(3. z.Z)

surface

voltage

(3.2.3)

sphere

(since

than

must

find

that

_(a)

this

this

are

the

the

of

of

of

if

the capacitance

— II. I millicoulombs.

distribution

by a capacitance

(3.2. 3) will determine

quite difficult to calculate.

shielding,

This

electrons

the whole

is surrounded

by a magnetic

by shielding

cloud

briefly

picture

without

Consider

is surrounded

capacitance

we

any

has

Now,

_(a)

wish

given

fixed

place

would

always

Shield,

discuss

through

vehicle

attract

factory.

coulombs

radiation

a general

as to make

the electron

b’ . The

a charge

maintain

example

rounding

between

charge,

model.

sphere

space

and

the

In this section

intended

of the Plasma

if the sphere

be Ii. I x 10 -3

electrostatic

as it stands,

of the magnitude

plasma

Radiation

the cloud

the electron

of the way

Q

two

can

are

are

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pure

with

must

from

which

space

— 222

across

field.

charge

as was

charge.

concept

of free

is not,

details.

useless.

described

explained

simulating

electrons,

is because

a positive

the charge

arrangement

geometrical

picofarads.

by a cloud

the voltage

arrangements

the required

in connection

In the Plasma

is distributed

considerations,

the arrangement

the geometrical

the surrounding

but the details

be characterized

first the situation

of the electrostatic

222 x 10 -12 farads

to be 5 x 107 volts,

of 5 x 107 volts between

the combination

millicoulombs.

if the large

by a larger

this is 444

that arises

difference

concentric

conducting

2 meters,

a -b- r

the two

overcomes

spheres

between

spheres

4=e0ab’

remains

Radiation

objection

of two

electrons

sphere

spheres.

entirely

follows

4=E0a

thereby

electric

Plasma

plasma

Shield

attract

Now,

b’-a

terms

Thus

does

field

and

that

and

not

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the

the

-ll-

is

In

of

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I

C

=

a

it

l

sphere

is

in

we

the

held

shall

cloud

being

being

satis-

Shield,

that if

However,

in which

so large

Radiation

to convey

at a rate

It follows

considered

C , which,

of the previous

of radius

a charge

requires

carries

(3.2.4)

no net

sphere

single

space

inner

from

sur-

the

the

the

To

to

to

is

picofarads.

the spheres

carries

confined

the

If b’ —4 meters

of - Z2. 2 miIlicoulombs,

a potential

of 22.2

it

two

until it penetrates

as it travels

sphere;

that the outer

energy

of the existence

will fall until it is brought

it will start to fall

of this sphere,

wil[ retain

at a potential

the potential

to protons;

The

rest

pure

back

If we

outer

sphere

regions

towards

5 x I07

continue

geometry

not only

spherical

of higher

volts above

representing

it will have

electrostatic

is transparent

in its further

of the spheres

at the surface

the electrostatic

ing the arrangement

by a distributed

vital question

is a function

of electrons

intensity.

separating

radiation

moderate

shield.

incoming

Poisson’s

number

meter)

parent

their

could

present

earlier.

they

held

given

are

the

In

to

is not representative

we

we

But

can

and

one.

than

have

even

ways

When

from

then

Then,

would

energy

surely

regard

5 x [0

kinetic

Suppose

already

Shield,

sphere.

sphere.

a large

vehicle.

distance

a proton

dismissed

Radiation

the outer

the outer

of 50 MeV

of 50 MeV

shielding)

is in many

its kinetic

the surface

it recrosses

volts higher

of the Plasma

of the Plasma

of “infinity”.

just discussed

for the reason

the possibility

At this point,

will be unaware

this difference,

its initia[ energy

by a n_agnetic

shall discuss

than a solid

the electron

ne(r)e ¢0

of electrons

of electrons

by “magic”

the moment

Therefore,

the inner

the o_ter

Radiation

exan_ple,

the mean

2 d6 dr

in place

Clearly,

in such

symmetric

discussion

in our

around

sphere

number

Shield

second

potential

connects

situation

(i.e.

Later

cloud

weigh

d dr

-12-

only

more

held

sense

have:

_<ith

r .

r

For

the

the

the

the

we

of

wc

we

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of

of

in

n

[

]

e

potential

of the inner

the outer

reacquired

travels.

example

aspects

to ignore

the space

radiation

the spheres

In the Plasma

cloud

to be distributed

density

in place

in detail.

protons

equation

spherically

to

of

as

of

the

into

sphere

sphere

Shield.

that the

approach-

it is also

this energy

is replaced

a cloud

reflection

trans-

density.

that

that

a fair idealization

though

Radiation

the inner

{in the discussion

material

sphere

field of

imagine

a manner

per cubic

shall just suppose

this obviously

is completely

proton

charge

be a solid electrode

that the insulators

The appropriate now be shown to be:

solution of Poisson’s equation, valid for a —< r _ b can

Now for simplicity,

a total charge

extending between the surface of the inner sphere (radius a )

and some larger outer sphere of the previous example;

electron cloud represents

the electron cloud therefore

n

e

density

“infinity”

potential

electric

inside

vario,:s

given

The

The

now

For

For

a

at r — b

=

Q

e

_(r)

(b -

r)Z(b

4_E0r

• r/Z)

is zero,

(b 3 _ a 3)

a3)ne

as is also

Q _ 4

the electron distribution

3 T,(b -

suppose that

• Q given by:

radius b . This distributed

of the “space

the potential

field also

is higher

be written

(b-a)(b+a/2)

electric

vanishes

vehicle”

is also

because

• a//b)2(1

= @(a)

variation

b2+ab+a

• 2b//a)

• 2b//r)

r//b)Z(1

there

4=_0a

across

zero

@(a)

for

The

-13-

_(a)

_(r)

d(r)

d(r)

this

can

the

b/a

of

of

in

in

Q

(l

(l

,

,

r

(3.

2.6)

> b .

(3.2.5)

is one of constant

the contains

b . It follows

the potential

electron

(3.2.

the

at

(3

”

.

of all points

is no net charge

r >

than

value

form:

field at r = b

this radius.

that the potential

by the amount

values

concentric

outer

the

• 2}m

density

cloud is shown in Fig. 3. 1.

Formula (3.2. 3) allows the calculation of an eq_iivalent capacitance

the system of sphere plus electron cloud bdven

to

of

If,

for

the

the

the

this

with

radius

for

example,

electrically

Comparing

Z millicoulombs

electrostatically

the moment

b = 5.46m

electrons/re.

volts/meter

Q = 22.

{ = 2”,t3

enormous

analysis.

required

uniform

electron

spheres

electric

present

surface

sphere

ponds

raises

cloud

cloud

come

shall

5 x

field

field

such

with

E(a)

The

just

and

tric

the

the

the

we

we

an

of

of

of

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is

a

radius

,

it

=

2

is

is

C

we

see

by:

by:

our

0 a

that

that

b_a

4_r_

from

cloud

given

sphere

sphere

_ a Z

(3.2.4),

follows

extends

electron

disc,lssed

distributed

b 2 _- ab

arrangement

arranRement

b 2 + ab + a 2

(b - a)(b + a/a)

: 4 meters.

electrons/cc.

.5 million

to which

calculated

obviously

extending

Radiation

electrons.

volts/cm.

electrons

numbers

equation

question

example

example

positive

= . 44

number

number

number

follows

quoted,

Shield”

electric

density

density

: g .

quoted

(3.2.4)

charge

charge

before

cloud;

taking

radius

exerts

return

radial

value

value

more

force

Thus

large

from

from

shall

find:

field

ratio

ratio

after

e of

This

total

This

over

5.46

own

-14-

also

The

that

Q/4

two

this

this

this

this

this

one

and

For

For

not

the

the

the

the

the

the

the

we

we

we

on

on

its

7a

of

of

of

of

of

of

in

to

of

Q

N

at

b’

is

is

is

=

x

n

x

x

a

e

a

a

”

to

an

where

• 2m

corres-

electron

coulombs/m

calculate

support

outside

matter,

value

equal

elec-

1 x

that

fact

For

out

the

the

the

the

5).

of

of

of

in

to

.

equivalent

earlier

a

: g

concentric

= 2.

electrons

The

trivial

surface

has

(in

the

10 .3

layer

3 = 2.1

Q/e

to

The

4_0a2 or

questions

observe

“Plasma

just

RADIUS OF ELECTRON CLOUD b

I!

._J <

r0

”-” O

to or tO r

Z to 0.5

_3 < I— _— Z w

Fig.

3.1

O.

A573t

/

/

a

_—=-=

POSITIVELY

CHARGED -.. SPHERE

from charge

sphere the

radius equal

a cloud

Distribution

potential

presence

uniform

electron

electron

positive

charged

outside

sphere.

(radius

charge

c[oud

to is

-15-

I I

:5

the

the

on

an

of

of

of

in

a

)

_

—r 5_

extending

negative

the

the

in

to

sphere

density

b

. The in magnitude

* II x 10 5 newtons/m 2-

can also

on the inner

The

at this pressure

preceding

situation

a preliminary

turn

electron

of attraction

the negative

is the same

the magnitude

v

to

in

to

we

the

the

3.3

The

The

also

For,

hold

and

the

The

used

tities

B ,

force

gives

electric

parallel

“Plasma

sphere

Magnetic

involved;

Radiation

sphere;

in which

problem.

a magnetic

this force

of as the force

electrons}

supposed

magnetic

nullified.

electrons

in Fig.

satisfies

become

outside

should

would

which

ways,

Thus,

given

those

away

tially

these

leads

force

there

from

least

field

both

loop

they

will

will

will

like

3.2.

this

due

one

one

but

the

the

are

(or

all

be

us

it.

to

to

in

to

at

B

space

reject

have

Field

.

_

in

to

of

in

of

of

an

an

no

on

-Q

+Q

are

the

the

the

has

any

this

-e(v

idea

next

This

field

from

force

gives

space

fields

cloud

place.

This

much

orders

x B)

B is

follow

charge

around

electric

exerted

Shield”

force

would

electron

direction

cloud.

charge

charge

spherical

geometry

important

indication

between

distributed

observation

by which

immediately

-e moving

a magnetic

the means

discussion

of magnitude

as to cause

not be such

the positive

in the electron

. II atmospheres.

of the electrostatic

as that of a gas atmosphere

the magnetic

of magnetic

accomplished

topologically

10 7 volts,

requirement

on which

observation

correspond

possibility

illustrated

additional

“infinity”

magnetic

spherical

in Fig.

potential

v x B

simplest

vehicle,

flowing

current,

electric

Plasma

vehicle

vehicle

surface

simple

single

really

them,

along

along

space

Now,

form,

place

since

same

short

there

large

what

lines

until

field

field

field

after

time

This

kind

only

very

5 x

line.

near

-16-

that

3.2.

that

that

and

one

and

and

and

can

can

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the

the

the

the

the

the

the

the

the

are

are

To

or,

by

no

by

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is

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a

a

a

requirement

field

and

be

respond

It

follows

portions

equipotentials.

differ

There

to make

of

field

of a structural

of

it

a

is

of

be

of

the

the

can

and

way

with

field,

quan-

near

essen-

velocity

nature

inside

be thought

magnetic

precise,

vehicle

variety

shown

Shield

thing,

space

place

same

form

lines

lines

field

field

that

coil

the

the

are

far

no

of

of

to

to

a

geometry

that

vehicle,

field

component

consequences.

magnetic

there

the

be

another

be more

in

loop

perpendicular

Radiation

Fig.

3.2

A74,’?

the requirements

of the magnetic

is the simplest

illustration

field lines

field shape

satisfying

Radiation

CURRENT

current

Shield.

LOOP

shows

shape

-17-

loop

form

This

A

the general

a loop.

giving

such

a

of magnet

of the Plasma

surrounding

of a topological

Radiation

as one might

not satisfying

a topological

3.4.

current

other

of Vehicle

that the configuration

A

tron

note

ways

from

from

second

general

second.

pending

heading

Several

3. 3 and

electric

electron

directly

of these

in Figs.

in favor

in which

although,

departure

of shapes

advantages

the Plasma

restrictive

is stationary.

is incomplete.

do not reach

expression

electric

standing

electron

Equating

seeking

(i.e.,

solar

flare

cloud

these

must

must

One

are

and

The

vehicle

is on examination

out direct

examples

a more

vehicles

5 under

the present,

advantages,

A brief

also

when

to counteract

further

observation

is

For

are

two

The

than

must

That

3.6.

have

two,

rule

these

about

torus

There

torus

rather

field.

(vx_B)

remain

study,

Shield

torus.

it does

of Fig.

a force

is zero

3.4 may

thinking

suppose,

required

although

is given

of space

Of these

important

discussed

condition

the shape

But since

importance

uncertain.

in Section

in Section

is obviously

Configuration

possibilities

that a space

Possibilities.

for the force

that the force

of considerable

this condition.

be a topological

can be deformed;

are an unlimited

of the expression

be {on the average)

the first represents

a static equilibrium.

to counterbalance

this is supposed

to the electric

of the magnetic

to be reached

on the basis

perpendicular

are briefly

the present

of a rather

complicated

equilibrium

48 hours).

comparable

concerning

conclusion

in a time

in motion

discussed

magnitude

problems

i_ = v/c

vehicle

present

E pc

:: E/v

nature

kind,

which

which

where

-18-

many

note

only

The

The

and

For

The

we

B

,

electron

and this motion

we

we

of

the

the

the

are

than

cloud

Thus,

shown

on an

number

not as

exerted

follows

utilizing

the elec-

discussion

adaptation

substantial

knowledge

(3. 3. l)

of the

of a

3.4

evB

is

eE

.

.

field that the electrons

to the duration

state of under-

in Section

that the dynamics

our present

of the force

force

is

the form

by a magnetic

a dynamic

be permanently

be so accurately

the space

about

of this dynamic

in the Appendix.

poses

further

force

yields

is quantitative.

field, the electrons

in motion.

f

Fig.

3.3

A2089

o *

CRYOGENIC INSULATION

”

DRIFT

.

°

°

”

..

o

;°.

i’:” *

-_

*” "":

CLOUD

\

ELECTRON

MAGNETIC FIELD

SUPERCONDUCTOR

superconducting

double-walled

*“OUTER

the many

in Section

symmetric

SHELL

SHELL

INNER

Radiation

discussed

direction

possible,

possible

azimuth

electron

magnet.

adapted

vehicle.

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current

vehicle

Shows

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shown

shown

shown

Shield

4-coil

cloud

space

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other

loop.

drift,

Also

loop

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Fig,

The

that

3.4.

this

and

the

the

the

are

are

Of

be

In

of

in

in

to

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realization.

associated

in Fig.

SHIP

more

axis

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can

3.2

the

the

the

the

for

its

of

of

is

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SPACE

INTERIOR

particular

around

with

arrangement

\

5- 6-EXIT

Fig.

3.4

A7807

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p _ 10”15 TORR

SPACE

OUTER

vehicle. a cTlindrical approach follow cloud,

are magnetic but are

conceptual space

alternate Shielded

field distinct

could merits

This launch

utilize of

7- EQUIPOTENTIAL

equipotentials

configuration

OF ELECTRON

II- ANTENNAS

8- MAGNETIC

INNER SKIN

discussed

electron

I0-LIMITS

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p,‘5 psi

STRUTS

OUTER

The

this

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of

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The

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lines

outside

SURFACES

FIELD LINES

9- LIVING 8 WORKING SPACE

INSULATING

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3- NON- BAKEABLE

4-BAKEABLE

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Possible Radiation uration relative 3.6. interior cloud.

can be as high

field of only

effect on the calculated

situation.

relativity)

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webers/m

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On

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a

_

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the

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theory

chosen

if we

large

depends

5 times

magnetic

perhaps

E = 5 x

unattractive.

the Plasma

understood.

massive

guessed

magnetic

magnetic

magnetic

optimum

element

Section

ticular,

smaller

factors

appear

item

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field

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3.6)

the

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fixed

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velocity.

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B

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But

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speed

value

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where

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weight

intense

devices

power

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volts/m

quoted.

already

absolute

it may

electron

electron

lacking;

a pure

strength

giving

magnetic

magnetic

required

k gauss

assuming

radiation

k gauss.

necessary

108m/sec.

Shield,

determine

knowledge

c = 3 x

as 0.9,

_ = l/Z),

permissible

assumption

comparable

a magnetic

the magnetic

insulation,

a considerable

the superconducting

all estimates

controls,

Radiation

the.Plasma

substantial

necessarily

dimension.

connection

meaningful

illustrated

following:

achievable

supply,

Shield.

A more

probably

Radiation

trade-off

magnetic

quantity

consider

desirable

although

in Fig.

1 ) are

systems

operate

based

energy.

largest

energy

to be

rather

values

would

utilize

larger

varies

have

been

study

Study

likely

linear

some

mean

field,

point

itself

_ (<

cube

Now

total

total

does

with

with

(and

-21-

this

this

this

low

and

not

the

the

the

the

3.4

the

Up

by

be

in

as

of

of

to

of

of

to

is

is

is

the

an

briefly

a

a

if

is

is

be

go

by

of

far

the

(by

the

the

the

can

also

that

give

case

one-

pure

field

Here

Note

have

way;

other

value

them

given

Using

below

would

makes

would

electro-

in this

weight

magnetic

magnetic

field coil

is the only

I. 9 k gauss.

important

represent

discussed

magnetic

It may

it has

Shield.

square

been

fields

fields

fully

very

over

The

par-

the

the

the

yet

an

in

In

of

of

of

magnetic

etc.)

to the present,

on this guess.

not

magnitude

the mean

magnitude

uncertainty

Radiation

(with its structure,

in the Plasma

_ = I/Z and

determine

A final

attainable,

to

volumes.

a deeper

configuration

in the

energy.

of

fundamental

sound

capable

solved

tendency

energy

quantitative

Specifically,

vehicle

cross

vehicle.

must

field)

of

the

tosses

magnitude

loss

electron

a

it

if

is

is

as

be

its

up

3.4

the

the

can

has

will

free

free

The

The

tant

field

with

from

from

must

work

turns

cloud

Shield

giving

strong

energy

actually

in this

certainly

magnetic

described

problems

unknown

associated

capability

restrictive.

Containment

thermodynamic

(10-30 k gauss)

acceptable

protective

electrons

duration

unstable.

seconds,

current

current

electric

dicular

current

would

speed

space

space

secs).

mum

about

secs/.

3.4.1

1/2c,

with

time

take

into

due

this

this

loss

and

the

the

the

far

.1_

the

By

all

1_

be

an

of

of

of

to

to

to

a

it

is

is

is

at

in

in

to

of

to

of

of

to

in

be

be

all

by

are

the

the

the

the

the

the

the

the

the

the

the

can

out

due

low

this

The

The

The

that

that

way

onto

idea

held

with

with

low”

view

turns

field.

basic

field;

cloud

point

small

cloud

place,

rates.

stated

Cloud

before

Plasma

Plasma

electric

concept

various

operate

interior

volume.

collapse

electron

although

shielded

available

problem

realized.

Electron

trade-off

principle.

electrons

tendency

assurance

relatively

However,

definition

Radiation

acceptably

underlying

in which

‘lacceptably

of holding

the means

the magnetic

the magnetic

substantially

the mean

mechanisms

we mean

constitutes

appropriate

a voltage

somewhat

extremely

possibility

dangerous

Radiation

collective

electrons

direction

accuracy

crossing

roughly

sp.eeds,

current.

If we

Plasma

to be

to be

to be

should

motion

1 part

around

charge

watts.

power

. 11_

cloud

in a

small

effect

flare.

short

Thus

some

solar

volts

Such

than

total

sees.

field

field

time

time

.022

5 x

drift

drift

that

that

take

this

loss

this

will

lost

less

not

Put

the

the

the

the

-22

5.5

are

By

be

be

all

an

of

of

of

to

of

in

in

at

is

if

a

a

°

most

electron

the magnetic

Instabilities

most

volume

Plasma

a magnetic

many

the

the

Radiation

electron

out

at

(and

comparison

2 days

coulombs,

yields

differently,

must

in

to

to

of

be

fall

and

will

this

that

very

very

field

large

allow

cloud

varies

Shield

Shield;

impor-

difficult

electron

Radiation

a distance

a maxi-

perpen-

Plainly,

Shield

hence

cloud

2 x

loss

the

the

the

(or

be

in

in

A

at

_

a

amps.

electron cloud could cause the cloud to fall across the magnetic field on a

large scale. But

instabilities

usual kind would be expected to correspond to the inherent

the electron cloud. time it

takes an electron to drift around the device (i.e.,

on the order of the . Ill sec), or,

the electron plasma period, or even the electron cyclotron

These times are so extremely

is vital

of the concept

the electron cloud be exceedingly stable.

that prolonged and careful study of the question of stability

consistently encouraging results. Ref. 48 to 53; but a summary of the results suggests that

The details of these studies are given in the inner edge

if

of the electron cloud is maintained very close to the surface of the space

stability

There is also empirical

device (the Vac-Ion Pump)

which is closely related to the

Plasma Radiation Shield is successful only because electron clouds of our

type are in fact very stable. Our own experiments have also suggested the

same, but there is an important proviso:

no experiments have been done in

the geometry demanded by the Plasma Radiation Shield concept. Since cer-

tain possible modes of instability

are strongly dependent on geometrical

it will ultimately

the stability of the Plasma

Radiation Shield in a direct manner. At present, all

that we can say is

that experimental,

evidences are all sufficiently

encouraging to proceed to other

forms of loss on the

assumption that stability

is discussed in somewhat greater detail 3.4.2

Diffusion

Classical

in the Appendix.

fact

vehicle,

small-scale

even shorter, period.

factors,

“classical

These

other

with

deal

We

(1)

(1)

of

it

that

that

short

can be attained.

These time scales are typically

the times associated with inherent

the hoped for stability

be necessary to test

is in fact present.

and theoretical

(generally

empirical,

slower)

temperature.

possibilities

collisions.

Collisions

diffusion,

collisions

generally

a very

density

neutral

caused

slower

source

atoms

order.

forms

other,

come

weak

close

ions;

from

form

only

than

-23-

loss

less

this

and

the

are

(2)

(3)

(4)

by

or

of

of

of

of

in

for

of the

has yielded

the success

time scales of

It is a fortunate

evidence that a

The question of

particles

indicate

heading

matter.

under

there

with

that

like

and

the

are

is

a

diffusion”

electrons;

these

Electron-electron

cause

gradient

losses

electrons

particulate

between

when

Calculations

1 watts,

is

is

in

of

of

are

the

the

and

that

also

(i.e.,

(2)

field

(3)

trons

other

space

cloud

sp_ce

electric

restrain

strongly

therefore

Radiation

Electron-ion

Electron-neutral

outgassing

generally

electrons

ponding

exposed

electron

fraction

ionized

if we

Shield

length

These

space

these

after

ion,

and

the

be

of

Shield

expelled

sufficiently

them.

on

ion

the

any

system.

field

effects,

vehicle

negligible,

concept

atoms,

speeds

to

to

have

take

time

be

of

ionization

will

unrestrained

well

electric

in

a

is

to

to

to

of

in

of

In

of

I0

of

-7

be

no

by

no

by

no

for

for

are

net

the

the

the

the

the

the

the

the

the

ion

but

are

due

and

UV

this

that

that

true

The

will

will

Due

ions

ions

outside

with

This

time

time

time

time

flare

field

have

from

from

solar

from

solar

from

from

from

there

other

close

leaks

order

cloud

might

These

atoms

atoms

cabin,

cloud.

space)

within

typical

neutral

density

coming

energy.

coming

positive

electron

ambient

massive

exposed

reasons:

problem

seconds,

reflected

surfaces.

radiation

diffusion

generally

exchange

residence

collisions

following

elastically

maximum

allowable

particular,

collisions.

collisions.

pressurized

the magnetic

electrons

the magnetic

be moving

temperature

circulating

a density

restriction

ionization

moderate,

following

generally

generally

108/cm”

suggests

reasons:

electron

electron

electron

positive

passage

become

account

coming

ionized

1 sec.

Plasma

elapses

surface

section

neutral

during

severe

before

across

cloud,

which

atoms

speed

speed

about

space

cross

atom

atom

atom

from

their

field

This

very

puts

flux

will

The

part

that

that

just

and

and

and

-24

ion

the

the

the

the

the

the

the

the

the

the

the

the

the

are

are

for

for

off

on

by

on

an

an

as

of

of

of

of

of

of

in

at

is

a

a

a

a

,

vehicle

ions

cannot

in

is

with

ions,

be

the

out

Radiation

flux

coming

it

is

cloud.

vehicle

cloud.

formed;

but

its

to

of

of

so

are

the

the

and

and

and

this

field

deep

elec-

rate.

short

present

Plasma

greater

came.

Now,

these

once

will

the

the

the

cm

off

at

If

,

corres-

1010cm/sec,”

-18

will

a non-negligible

(4)

mass, will be ejected into deep space by the electric

the time 10

seconds previously quoted. But

a positive ion from some point rear

the surface of the space

vehicle to infinity electrons from the outer

is just as much a loss as is the transport

of regions of the cloud to the surface of

the space vehicle.

the ions are formed

right at the surface of the space vehicle and subsequently ejected across the full 5 x 107 volts.

In this case the limit on

the current of ions is about mum allowable number of such ions on the order of 1012/sec,

. lgt amps. This represents a maxi-

and this is also the maximum allowable rate of escape of

neutral atoms from the active space vehicle. of oxygen from the cabin, rate of about 10-6 grams of oxygen in two days!

this is a leak it corresponds to an allowable leak the

In fact,

If

mean potential at which neutrals are ionized can be considerably lower

since in the 1 sec mean free time

than 5 x l07 volts,

estimated above the neutrals would cover a distance like 100 m.

instance, or more. ionization is only 1% of the full voltage, or 5 x 105 volts.

the mean potential of

Suppose,

for

tolerable current is then 10_1amps corresponding to a flux of 1014,/sec, or 10-4 gins in 2 days. However, even with these

figures, high quality vacuum vessel;

the cabin pressure vessel must be a

is double-walled,

this low leak rate should be attainable.

There is also a severe

restriction

on the amount of outgassing of the whole surface

that can be permitted;

over the surface of about not unattainable level.

roughly to a pressure

mm Hg, again a very low but

It must be remembered that ample time

is generally available to bake and thoroughly clean all exposed surfaces before activation of the Plasma Radiation Shield. We

-7

In the worst case, all

return to this question in Section 7.

this corresponds -12

is obvious that

that

particles

surface

matter.

should

clean,

l0

dust

-25-

the

the

it

if

it

no

be

of

is

If

of

field in

the transport

however,

Radiation

The

on

it;

shall

Particulate

Shield

Plasma

present

There

If, as is

2/year

should

might

perhaps

coinciding

of classical

is the control

that this problem

are

electrostatic

any yet achieved

contemplate

At this stage

preliminary

achieve

believed,

the immediate

problem

the electric

or less,

completes

important

Although

the actual

3.5

and

This

solar

then,

It was

shielding)

in Section

Achievement

outgassing.

insuperable;

by far the most

applicability

do no more

experiments

mechanical

available

guarantee

electrode

electrons

machines

parallel

reaching

to ask,

natural

limited

between

earth,

these

which

there

been

best

and

can

day

are

low.

take

than

from

than

with

from

High

flare

would

there

arisen

space.

degree

higher

applies

comment

to have

of such

A large

voltages

Voltages

an event

meteorite

be stated

difficulty

activation

in Section

field, and

constraints

of problems

I0 -8 gm/cm

reactivation

neighborhood

field should

the required

this source.

is reasonably

of the earth,

our discussion

of cleanliness.

of the electric

2 (in connection

but the probability

difficult, it cannot

55 this flux is less

the flux of micrometeorites

that it is likely to impose

for an experiment.

as field emission.

can be reached.

the achievement

is encouraging,

is as follows:

circumstances,

to the Plasma

in the Plasma

to the Plasma

it is that we

of breakdown.

the electric

field points

the effects

this occurs

is actually

limitations

conditions.

particular

are those

Radiation

Radiation

Radiation

voltages

voltages

relevant

in high

in such

of high

Shield.

explain

Shield.

current

having

vacuum

56 -64

drawn

known

-26 -

most

This

This

how

can

The

why

are

A

of Very

mentioned

that the required

the same

in these

voltages

than

do not apply

of known

that the required

can be no substitute

In general,

by problems

which

electrodes

theory 56 of how

{or cathode)

out of the surface.

mechanism

a

to

on

is

with

help

It is

be no

outside

Shield.

an hour

remains,

reviewed

shut off

diffusion;

of leakage

in present-

as to draw

breakdown

breakdown

that the

depends

not a

lack

has

we

of

in

is an area

in the laboratory

to do with

It seems

at the negative

a direction

by the quantum-

current

that limit the voltage

This

but is obviously

field is intensified.

by Ohmic

to evaporate

formed.

is reason

is no material

electrode

occur.

itself, and this is the anode

that is the direction

that it tries

viewpoint,

The

and a tiny anode

This

field is on the order

that contemplated

this field strength

that is, on the

on the electric

concentrated

field strength

altogether;

the true

ions by field emission

field strength

electric

ion current

Radiation

forces

projections

the current

o

anode

there

where

Next,

scopic

million

regards

extract

material

jections

positive

volts/cm,

optimistic

electrode);

of positive

an enormous

satisfactory

exponentially

At a certain

this is indeed

ion microscope,

I volt/angstrom.

only be proved

electrostatic

the Plasma

breakdown

of these

reasons.

lattice,

subject,

reasons

current

lative,

order

ions

and

The

3.6

The

Possibilities

ions.

can

than

when

thus

then

them

only

From

there

heats

these

where

Shield

occurs

Shield.

greater

cathode

vehicle

cathode

through

is from

a large

a device

in which

at which

Radiation

mechanism

breakdown

field and

100 times

the Plasma

in the gas

limitations

impossible.

projections

the working

Furthermore,

is virtually

is therefore

this heating

the electric

the electric

is the space

of breakdown,

a field some

on the order

is concerned,

is sufficient

field is such

field emission

of the latter.

on the cathode

of the electric

a quantum-mechanical

field at the surface

field of this strength.

for the Configuration

by an appropriate

to offer herewith

it is worthwhile

and the second

not be subject

by an electric

for the moment

as a typical

contemplated.

atmospheres,

accomplishes

it is again

understood,

experiment.

I angstrom

materials.

discussion

Radiation

of 3,000

general.

strength

3.4 may

of Fig.

of most

of Fig.

spacing

binding

energy,

before,

Taking

Shield

should

should

stated

-27-

This

turn

must

and

3.4

two

The

As

I volt as a typical

can be drawn

the Plasma

for this possibility

but nevertheless

at the field strengths

sound

of the yield

Microscopically,

a

as

to

if

for

The

only

Now,

draws

case,

to be

device

of 100

produce

produces

evidence

the pro-

{positive

at micro-

for in our

dissipation.

the extraction

of the positive

is that if the

advantageous.

discussion

as specu-

of which

up this

an ion

vacuum

hopes

it is

in a

ions

why

sum

can

these

the first is specific

first purpose

as it is presently

not lose appreciable

between

plain

To

to high

be regarded

some

purposes,

configuration

out to be very

Shield

there

to

definition;

as well

stated

following

shown

volume

themselves

the

of

is

the

imagine

are

the

to

to

to

of

an

for

for

are

the

the

the

not

that

that

axis

This

true,

been

have

wish

were

from

must

large

large

yield

ideas

radial

locate

Plasma

It was

suggests

attracted

instance,

distance,

electrons

example,

complete

otherwise

Radiation

symmetry

anticipated

advantages

imaginative

representative

fall inside

the magnetic

equipotentials

situation

important

interpretation

tangent

potential

defining

possible

satisfies

vehicle,

contour

would

region

where

but,

being

space

there

netic

lines

field

field

field

near

that

the

the

are

of

in

to

is

the

a

a

is

is

at

l}

to

in

in

to

to

of

as

of

of

so

be

be

be

its

up

on

on

far

for

the

the

the

the

the

the

the

the

can

this

that

still

The

The

will

But

may

3.2}

hold

This

field

field

rlarg

lines

lines

(say,

front

case.

large

from

quite

since

close

away

room

small

study

space

cloud

rsmal

under

radial

might

show,

charge

further

further

axially

second

overall

Shield.

vehicle

Plasma

simpler

amount

volume

largely,

achieve

concept

roughly

vehicle,

purpose

positive

magnet.

electron

changes

reasons:

distance

in Fig.

confined

electrons

a broad

magnetic

magnetic

magnetic

, where

statement

Radiation

symmetric

3. Z that

desirability.

in Section

substantially

characteristic

configuration

equipotentials.

e = V/(2=r_mall)

that it is, the configuration

field at the boundary

su_zh an electron

of the electron

in the vacuum

as follows:

field lines

properties

equipotentiats,

equipotentials

shielding

for sure

requirement.

in Section

of Fig.

throughout

region,

whether

electrons.

electrons,

statement

boundary

equation.

magnetic

magnetic

magnetic

entirely,

follows:

electron

electron

-28 -

regions

outside

indeed

follow

cloud,

about

some

field,

V ,

there

even

such

then

case

axis

free

that

that

that

this

and

but

but

the

the

the

the

the

the

the

the

no

no

or

of

as

of

of

of

In

in

is

is

application

still

not

on which

pass

at

of

electrons

remainder

the magnetic

V is

a

a

is

e.

to

of

of

as

be

be

o_

far

the

the

(as,

still

near

than

may

very

rlarg

there

close

fields

cloud

might

study,

region

strictly

expected

by means

is possible,

become

would

cloud,

This

have

Thus,

some

mag-

lines

lines

field

The

of

it

field

electrostatic

equipotentials

but would

cloud.

cloud

3.4 would

Laplace’s

the magnetic

to the magnetic

It is not known

on the assumption

advantages,

not affect the basic

of the configuration.

I. The shape of the magnetic field is roughly that of a long sol-

enoid; in such a magnetic field, distances than they would, say,

the field lines close at for

the loop current of Fig. 3.2.

the electron cloud should be substantially

2. The general shape of the space vehicle is cylindrical,

dance with many current

ideas about such vehicles; such a shape

is naturally

compatible with launching rockets.

3. The construction of a solenoidal magnet

is a simpler

structurally

than the construction of the four-coil magnet of

Fig. 3. 3. Also, volume would be very small

the stray magnetic fields in the shielded

4. Since there is essentially no electron cloud outside the vehicle, gas atoms coming from the vehicle will not be ionized, and will

therefore constitute no electrical

Thus,

lem (discussed briefly

in Section 3.4.2, and in detail

7. would be confined to the relatively

small area of the space

particular,

Thus, interior

loss.

indeed.

of the solenoid.

-29-

tolerated, cloud.

simple.

In particular, vehicle facing the electron cloud. antennas, etc. could be located on the exterior

the necessity for special sealing.

task

larger

in accor-

in Section

confined to the

the vacuum prob-

ports, doors, surface without

Even less

In

6. The injection of the electrons could be accomplished in the low

field region outside the vehicle;

these electrons would then

quite naturally the solenoid. Such an injection procedure might be extremely

proceed to the high magnetic field region inside

equilibrium we are considering has not yet been demonstrated.

is known about possible instabilities

of such equilibrium configurations.

we do not yet know how to calculate the shielded volume

5. The electric

field on the outside of the space vehicle would be

quite low. Thus protuberances of various sorts could easily be

and would have essentially no effect on the electron

In conclusion, we must emphasize that

the existence of the type of

detail in Section

size is set fundamentally

but the shape

3. 3. by the

Parameters

basic

first, the size and

is set by considering

and allowable

associated with such a configuration, vehicle can be tolerated.

i.e., what outer radius of the space

An important effect of this ignorance is that

calculations of the weight of such a Plasma Radiation Shield are irrelevant to the extent that we cannot associate them with definite values of the

a rough measure of the present degree of definition of the Plasma Radiation

Lastly,

can be taken as

The

tage

are,

most

nature

Design

mission

flares,

in some

possible

of solar

discussed

duration,

requirement

are far from

of the mission

3.7 Basic

shielded volume.

Shielding concept.

itself is proportional

in the Plasma

refrigerator)

the shielded

to calculate

uncertainty

ally from

field and

structure

primarily

magnetic

position

magnetic

required

Section

systems

_ (Eq.

volume

weight

scale

value

lack

Now

of

with

depends

Radiation

toroidal.

but these

This

size

are

and

The

3.4,

such

shown

doses

Shield

shape,

design

object

second,

3. 3 and

voltage.

in Figs.

the crew

Radiation

radiation

frequency

questions

especially

parameters

in Section

the overall

to the crew.

of the Plasma

as the actual

be essentially

to be undertaken,

the possibilities.

is set (as discussed

the extent of these uncertainties

on the coil configuration.

with the configuration

of the cryogenic

of any analysis

of the overall

this parameter

of definition

configuration

the shielded

of its power

of a Plasma

be a curve

uncertainty

the weight

quantities

associated

determines

discussed

Radiation

basically

of these

However,

strongly

of Fig.

, while

showing

weight.

a lack

weight

system

Shield

either

volume

cloud.

weight

weight

coil.

-30-

with

Lack

must

with

3.4,

from

any

was

The

The

_-2

The

The

[5

we

-i

to

and the systems

precision.

is

Two

and

The

vol-

Shield

by the

subject

spectra

and the

inherent

suggestions

(including

vehicle,

between

resides

of the

basic-

and

The

the

in

of certainty

briefly

but stems

of the space

with

of the attainable

the level

Shield

supply

of the possibilities

the relation

are not yet in a

that the Plasma

configurations

exhausting

a principal

Radiation

of definition

electron

stems

3.3. I), since

field.

in the superconducting

of the superconductor

associated

3.6 in connection

configuration

the

net

time,

precision

advantages

a much

question

accomplish

leave

the

the

sample

presently

a

it

is

to

in

as

of

of

we

the

the

the

the

the

any

this

The

than

such

eters

more

again

curve

about

Since

rather

placed

ments.

clearly

present

volume

purpose

shielded

weights,

establish

dependence

components

Summary

follows:

seem

3.8

not

To

as

a weight

with

is

Radiation

of weight

concept

possible

Preface

systems

calculating

characteristic

not

a

it

it

it

is

is

is

to

in

to

to

to

in

it.

In

of

of

of

of

of

of

as

as

as

as

be

be

be

do

on

for

for

for

for

we

the

the

the

lay

the

the

the

our

can

this

that

that

that

part

was

The

was

Fig.

also

now

may

than

with

This

such

such

done

here,

case,

basis

Thus

basis

these

paper

paper

curve

result

being

stated

which

assign

makes

design

results

weight

drawn,

magnet

system,

current.

weights

weights

sounder

systems

difficult

possible

physical

different

justified.

calculate

penalties

in Ref.

formulas,

particular,

associated

a Plasma

a Plasma

calculated,

reproduced

integration;

framework.

the most

components

considerations

the meridional

Characteristic

considered.

determined

necessarily

magnitude

1 million

(generally

Potentials

volts/cm.

magnetic

electrons

toroidal;

required

electron

positive

features

voltage

smaller

ampere

million

Plasma

vehicle

vehicle

several

extent)

(which

radius,

charge

charge

shape,

cloud.

shape

space

space

some

order

basic

force

volts

from

up,

with

total

The

line

and

and

has

-31

the

the

the

the

the

the

the

the

are

(to

-Q

by

on

its

of

of

of

of

of

of

of

of

of

of

in

Q

is

is

is

it

a

a

at

to

to

to

as

l),

up

vs.

the

not

has

and

this

3.5,

take

with

does

other

“been

study,

Shield

system

Shield.

param-

attempt

require-

vacuum

(Section

showing

possible,

indicates

Radiation

a magnetic

a knowl-

around

Shield

distri-

fields

away

field.

large

must

from

say,

size

and

the

the

are

to,

by

by

its

its

of

a

section

electric

Radiation

held

+Q)

roughly

vehicle

details

carries

turns}

sum

A cloud

space

field.

edge

and

bution

million

are

The

current

major

coincide

_- PURE MAGNETIC

SHIELDING

DESIGN

3.5

Fig.

I

I

‘,2OgO

3 MAN CELLAR

…-’

—_\

SOLID

PLASMA

ENERGYJ

SHIELDING

SHIELDING_

PROTON 200 MeV

of a Plasma

reproduced

comparison

reasonable

Radiation

Radiation

SHIELDED

shielded

estimate

regarded

magnetic

shields,

it must

VOLUME

Shield,

subject

pending

volume.

-32-

of the

Shield

curve,

weight

Shown

solid

more

pure

This

most

Thus

M 3

and

the

for

are

for

I00

as

be

as

I

[

I

I

i

±__L tO

The

the

remains

Plasma

studies.

for

energy.

uncertainties.

to large

weights

systems

design

of a

IOOO

from

Ref.

44,

of

J

;

’

a function

weight

detailed

estimated

MeV

Magnetic

of

whole

unknowns;

I.

It

two

The

large

be

is

around

although

optimistic

the

paper,

Even

satisfactorily

porate

would

affecting

are

detail

tant

the

over-all

Radiation

a detailed

however,

demands

possible,

question

particular,

discussed

above

true

function

being

“boundary

a

if

at

to

in

in

of

of

or

of

as

as

be

an

on

all

all

on

far

for

for

are

are

are

are

the

the

the

the

the

the

the

the

the

not

not

our

and

any

and

this

that

that

still

will

will

very

arise

pro’s

there

these

order

space

fields

know

con’s.

under

under

Some

score.

actual

gauss.

Shield

Shield

design

certain

remain

exactly

present

vehicle

Plasma

Plasma

various

reasons

involve

concept

guarded

grounds

follows:

it will

required

Whether

reaching

certainly

resolved,

questions

questions

optimism

Shielding

Radiation

Radiation

Radiation

especially

conditions

a whole.

Appendix.

acceptable

a Plasma

concessions

a position

advantages

demanded

Radiation

Shielding

discussed

provision

demands

demands

adequate

concept.

weights

relative

Plasma

vehicle

Shield.

design

large,

terms

could

space

study

fairly

these

solid

what

well

-33-

We

not

the

the

the

yet

the

the

are

are

are

are

we

To

by

be

In

of

of

of

of

in

in

to

in

to

it

be worthwhile

several

is

electron

space

it

is

to

in

in

of

are

the

and

that

that

later

with

topic

these

arise,

cloud

incor-

would

impor-

vehicle

balancing

guardedly

thousands

associated

conditions

conditions”

of weight

satisfactorily,

undertake

shielding.

presently

sections.

concept;

Plasma

extent

about

adapt

the

the

the

to

to

If

following

of

ready

this

specific

the

4. VOLTAGE SELECTION IN THE PLASMA RADIATION SHIELD

Radiation

of the voltage.

into the selection

8 of Ref.

shielding

— e.g.,

for all the principal

stipulates

dose

we

one

mum

The

The

dose

acute

If one

section

voltage.

to which

can then

the over-all

the biological

this criterion.

this thickness.

its skin and

range-energy

configuratio

of aluminum

Radiation

example,

protons.

required

strongly

the use

66 rad.

to stop

during

solids

Now,

bulk

rad.

Ref.

dose

66,

and

For

was

two

size

discuss

starting

the crew

doses

determine

determine

Shielding

Ref.

for any

Also,

any

If it is assumed

shielding

tables

some

As

One

may

and

and

over

dose

from

bulk

sort

some

most

enter

flare

solar

enter

which

basic

energy

proton

events

behind

shape,

various

of bulk

of dose

February

In Table

shielding

criterion

tolerance

can then

sustained

cumulative

parameters

the maximum

range-energy

or a maximum

the thickness

the magnitude

of the Plasma

be subjected.

of the maximum

the considerations

a first approximation

point is a consideration

that this thickness

of fast particles

that the maximum

for the same

is relatively

is relatively

is I0 gm/cm

of stopping

Conversely,

be capable

that these

of energy.

efficient.

equipment.

a certain

of energy

of proton

wasteful.

thickness

shielding

(actually

shielding

the same

30 shows

of solid

Further,

consider

separate

function

two-year

at high

surface

figures

amount

system

should

single

source

period

shows

Thus,

event

three

shows

-35-

This

dose

may

may

we

that the maximum

is adequate

the rate of loss

decreasing

protons

of solid shielding

n will possess

other

by

—

as

are

such

time

listed

period

Shield

of the

30 are

a maxi-

In this

to October

permissible

that a Plasma

configurations

in one week)

in the form

the use of

cumulative

Reference

I00 Mev

to stop

roughly

energy,

vehicle

proton.

10gm/cm

at low

behind

space

is a

then

any

the

was

to

at

of

this same

dose

events

configuration

are toIerable,

2 of aluminum.

in matter

energy,

shielding

be estimated

that witl just satisfy

tables,

that is stopped

I00 MeV protons.

2-4 gm/cm2-

range-energy

range-energy

Corresponds

of solid

a space

;’._ For

of any

power

have

We

shielding.

aluminum.”:” Suppose,

is required to stop

reference to the

tables shows that this thickness will

just stop a 40 MeV proton.

is therefore only necessary to provide 60 million volts of potential

It Plasma Radiation Shield in order

to achieve the desired effect.

100 MeV proton crosses the Plasma Radiation Shield voltage, The remaining 40 MeV are then absorbed in the 2 gm/cm 2 of skin.

skin thickness is 4 gm/cm Z, reference to the range-energy

tables shows

this thickness will stop a 60 MeV proton.

that Radiation Shield outside of 4 gm/cm Z of skin would also suffice to stop

Thus a 40 MV Plasma

I00 MeV incident protons.

Proceeding in this way, one can, using the

tables, construct a graph showing the different

of Plasma Radiation Shield voltage and solid shielding thickness that will

stop a given proton. by looking along the line marked “Proton Energy I00 MeV,” examples just discussed of a vehicle skin of 2 or 4 gms/cm 2, with Plasma

This graph is presented in Fig. 4. I. From it we can,

find the two

Radiation Shield voltages of 60 and 40 million volts respectively.

way to look at Fig. 4. I is to consider

the relative effectiveness of, say, a

40 million volts Plasma Radiation Shie|d against protons of various energies. I0 gm/cm 2 of solid shield- For example,

to stop a 100 MeV proton requires

ing. But we saw above that 40 MV Plasma Radiation Shielding ahead of 4 gm/cm 2 of skin will also stop a I00 MeV proton.

In a sense,

Plasma Radiation Shield is the equivalent of 6 gm/cm of solid shielding. Again,

to stop a 150 MeV proton requires

19 gm/cm 2 of solid shielding.

But a 40 MV Plasma Radiation Shield will cut a 150 MeV proton down to If0 MeV, and to stop a if0 MeV proton requires only 12 gm/cm 2. At this level,

the 40 MV Plasma Radiation Shield is the equivalent of 7 gm/cm 2

it

If

that

for example,

the skin thickness is 2 gm/cm 2,

that one need

to calculate

combination

a surface

determine

of 4 x I

in order

of 8,000

having

16,000

-36-

only

06cm

area

and

2

the

in the

Another

The incident

combinations

losing 60 MeV. If

the 40 MV

gm/cm

assumed

shielding

the total stopping

its shielding

vehicle

to total weights

, 2-4

kg respectively.

Fig.

4.1

A743t

Z

J

A @4 E

U

E

v

(.9 Z

.J W

(;9

,%

.J o (Jr)

I0

25

2O

(MeV)

ENERGY

PROTON

required tage

shields bination.

NG VOLTAGE

“Range-Energy

corresponding

RADIATION

effectiveness

electrostatic

electrostatic

proportions

appropriate

PLASMA

Following

Reversing

SHIELDI

shielding.

30 MV

a given

different

assumes

reduces

Tables”

energy,

outside

proton.

matter.

greatly

proton

graph

• 37-

solid

Note

solid

Note

stop

first

that

120

also

two

and

I00

the

the

the

the

the

the

the

the

the

40

60

Z0

of

to

of

or

of

to

to

is

0

a

shielding

components

shielding.

potential

advan-

relative

curves

order

given

com-

may

read

the

the

off

of

of

a

(MeV)

combination

one

great

electrostatic

the

of

incident

any

just

combinations

energy.

2 of aluminum.

effects

above

protons

consider

given

but this effect is relatively

This

in

not

spectrum

just stop

these

having

shield

it

is

is

is

To

the

protons

soft,

given

effect

affect

(since

make

solid

these

because

Plasma

exhibited

However,

shield,

shields

differently

a 60 MV

composite

energetic

effectiveness.

flux of protons

E 0 + dE 0

is any

grated

particles

particles

Later

Plasma

IREF

space

The

ERE

on,

flux

flux

was

free

Let

the

is

of

of

F

Radiation

n

=

is

at

in

in

of

be

by

all

the

the

the

the

and

this

4.2,

true

true

case

E 0

are

will,

dose

soft}

since

those

Table

above

more

high

from

more

where

which

nearly

cut-off

strictly

spectra

4. I.

space

small

their

ahead

protons

general,

particles

different

in Fig.

IRE F

energy

Shield

consider,

shielding

delivered

1. We

removes

in free

100 MeV

spectrum

protons;

for very

specific,

different

I0( > F,0}

of 2 gm/cm

an integral

At energies

the incident

considerations

listed in Table

[EEEF]

no special

but these

reference

(in MeV),

energies

energies

a voltage

in free

greater

choices

Radiation

Radiation

energy

having

choose

having

simplest

case,

space

Plasma

Plasma

behind

energy

Shield

Shield

whose

model

would

shah

have

EREF

dE 0

There

V .

have

V .

and

ERE

per

sq.

than

-38-

E l

n_- I

The

the

the

cm

we

dE

be

F

0

,

behind

with

dl 0

dE

Radiation

less

convenient

flux of particles

for a specific

= 108 protons/cm

flux of particles

is

for

by

energies.

will

This

the

the

point

than

Both

arrive.

example,

spectrum

I00 MeV

on more

an incident

is the inte-

consider

Shield,

than

F .

ERE

and

and

E 0

then

E 0

the

(4.

no

be

in

to

IRE F

= I00 MeV,

validity

between

will

energy

to

10 gm/cm 2 Aluminum

E2 _Energy

behind shield /‘_I”_E2

Plasma Radiation Shield, 60 MV

E1

2 gm/cm 2 Aluminum

Fig.

4.2

A7681

Incident Energy_

Schematic stop to Plasma

consists of Z gm/cm

of protons. Shield

100 MeV Radiation

shields Shield

diagram

consists

protons

spectra

shields

gm/cm

effects

Shield

ahead

ferent

2 of

these

have

such

each

-39-

two

that

and

the

are

on

on

of

of

II

I

Shield I

E0

Shield II

the ability a 60 MV aluminum.

> 100 MeV,

of 2 of

text.

The

dif-

the

in

having

aluminum.

protons

discussed

E 2

Mev

20

100

200

1000

I

0

E

E

Mev

Mev

47

II

|00

100

127

110

E 0

Mev

4. I

Shield

TABLE

Shieid

of Shield

Comparison

Effectiveness

1020

106[

-40-

206

149

266

218

190

An

field.

at

trend

with

Shield

the

in matter

equal the flux of particles with energy in free space. However, this approach would yield a finite flux of particles with low energy behind

(E1 + V)

the Plasma Radiation Shield and does not do justice to the properties

shield.

having an energy just greater

free space will be strongly deflected by the electric penetrate it

accurately

motion

initial

their

if

is

field, and can only

is

to

of

for

the

Use

line.

field

right

ticles

unity.

energy

greater

general

through

particles

probably

Radiation

is much

electrostatic

emerging

material,

protons

energy

power

where

shield

solid

from

and

For

the

the

of

of

of

is

x

than

is

is

is

is

of

or

of

of

of

by

for

for

the

the

the

the

by:

this

just

this

free

flux

E 0

than

This

dEl

n+2

least

V ,

more

(E 0

space

given

effect

factor

factor

factor

yields

dE 1

energy

greater

correct

strictly

dIl(E1)

parallel

E0(>V)

reduced

strength

estimate

deflection

deflection,