Alfonso Tarditi (1)

Plasma Technologies for Aerospace Applications

Alfonso G. Tarditi

Engineering and Science Contract Group NASA Johnson Space Center and University of Houston, Clear Lake

* Plasmas

Main Thrust for Plasma Research: Fusion Energy
Aerospace Applications
Research at UHCL

Outline

Plasmas

The “Fourth State” of the Matter

The matter in “ordinary” conditions presents itself in three fundamental states of aggregation: solid, liquid and gas.
These different states are characterized by different levels of

bonding among the molecules. In general, by increasing the temperature (=average molecular kinetic energy) a phase transition occurs, from solid, to liquid, to gas.

A further increase of temperature increases the collisional rate

and then the degree of ionization of the gas.

The “Fourth State” of the Matter (II)

The plasma state does not exhibit a different state of
The ionized gas could then become a plasma if the proper

conditions for density, temperature and characteristic length are met (quasineutrality, collective behavior).

aggregation but it is characterized by a different behavior when subjected to electromagnetic fields.

The “Fourth State” of the Matter (III)

Plasmas (V)

move in presence of electric forces

An ionized gas has a certain amount of free charges that can

Debye Shielding

* Shielding effect: the free charges move towards a perturbing charge to produce, at a large enough distance lD, (almost) a neutralization of the electric field.

E~0

Debye Shielding (II)

is called the (electron) Debye length of the plasma

The quantity

Debye Shielding (IV)

The Debye length is a measure of the effective shielding length beyond which the electron motions are shielding charge density fluctuations in the plasma

02BDeekTnql* Typical values of the Debye Length under different conditions:

Interstellar Solar Wind Solar Corona Solar atmosphere Magnetosphere Ionosphere

n [m-3] T[eV] Debye Length [m]

Debye Shielding (IV)

107

1020

1012

10-1

102

103 10-1

10 10-1 10-6

10-3

expected amount of ionization:

neutrals, (positive) ions and electrons.

From Ionized Gas to Plasma

An ionized gas is characterized, in general, by a mixture of
For a gas in thermal equilibrium the Saha equation gives the
The Saha equation describes an equilibrium situation between

ionization and (ion-electron) recombination rates.

/2213/22.410iBUkTinnnTeFrom Ionized Gas to Plasma (II)

(Long range) Coulomb force between two charged particles q1 and q2 at distance r:

12204qqFrFrom Ionized Gas to Plasma (III)

(Short range) force between two neutral atoms (e.g. from Lenard-Jones interatomic potential model)

repulsive

attractive

From Ionized Gas to Plasma

If L is the typical dimension of the ionized gas, a condition for an ionized gas to be “quasineutral” is:

The “collective effects” are dominant in an ionized gas if the

number of particles in a volume of characteristic length equal to the Debye length (Debye sphere) is large:

ND is called “plasma parameter”

3413DDNnlDLlFrom Ionized Gas to Plasma (II)

A plasma is an ionized gas that is “quasineutral” and is dominated by “collective effects” is called a plasma:

DLl3413DDNnlFrom Ionized Gas to Plasma (III)

An ionized gas is not necessarily a plasma
An ionized gas can exhibit a “collective behavior” when the long-range electric forces are sufficient to maintain overall neutrality
An ionized gas could appear quasineutral if the charge density fluctuations are contained in a limited region of space
A plasma is an ionized gas that exhibits a collective

behavior and is quasineutral

Force on a charged particle in a magnetic field

Plasma Confinement: the Lorentz Force

F = q v x B

Plasma Confinement: the Magnetic Mirror

Magnetic Mirror: charged particles (protons and electrons) move in helical orbits at their cyclotron frequency

Main Thrust for Plasma Research: Fusion Energy

The Bad Stuff

[Ref: Fusion Power Associates, http://fusionpower.org]

[Ref: US DoE, 1999]

The Bad Stuff

U.S. Fusion Budget Vs. the Price of Crude Oil

[Ref: US DoE, 1999]

The Bad Stuff

World Magnetic Fusion Effort (1999)

The Fusion Energy Hope

[Ref: Fusion Power Associates, http://fusionpower.org]

The Fusion Energy Hope

[Ref: US DoE, 1999]

The Fusion Energy Hope

The Advantages of Fusion Energy

The Fusion Process

Deuterium Tritium Fusion

How to Achieve Nuclear Fusion

Fusion Works

The Sun: a very old fusion reactor

Fusion Works

Controlled Fusion Experiments

Joint European Torus (JET), Culham, UK

Controlled Fusion Experiments

Inertial confinement: the 192 laser beams in the National Ignition Facility (LLNL) heat the inside surface of a hohlraum with high uniformity

Controlled Fusion Experiments

Inertial confinement: the target chamber in the National Ignition Facility (LLNL)

Aerospace Applications

Lightning Protection
Airfoils for Super/Hypersonic Flight
MHD/Chemical Plasma Propulsion
Plasma Spacecraft Interactions
Electric Propulsion

Lightning Plasma Channel

* Lightning affect spacecrafts:

Lightning Plasma Channel

Apollo 12

Space Shuttle

[1] S. I. Braginskii, Sov. Phys. JETP 7 ,

[2] M. N. Plooster, Phys. Fluids 14, 2111

Lightning Plasma Channel (II)

Objective: improve current fluid dynamic models [1-3] with prescribed current waveforms to a self-consistent plasma channel in a neutral background

1068 (1958).

(1971)

Idealized lightning current waveform

[3] A. H. Paxton, R. L. Gardner, and L.

Baker, Phys. Fluids 29, 2736 (1986)

Lightning Plasma Channel (III)

“Stuff” happens:

Lightning Plasma Channel (IV)

Current Interest: Constellation Program Lightning Protection Design

Plasma Airfoils for Super/Hypersonic Flight

a) Plasma off.

Plasma Airfoils/Actuators

b) Plasma on

Subsonic Plasma Aerodynamics for Flight Control of Aircraft: Surface plasma induced flow re-attachment of an airfoil at an angle to the oncoming free-stream (University of Tennessee).

MHD HYPERSONIC FLOW CONTROL (Russian Academy of Sciences, Moscow, Russia

Plasma Airfoils/Actuators

General Test Bed Arrangement for Wedge Model MHD Flow Interaction Experiments

Plasma Airfoils/Actuators

A concept of On-Board surface MHD Generator on a Re-Entry vehicle.

Plasma Airfoils/Actuators

Experimental Photographs of Wedge Model Test (Right Side Photo Images - Left Side Spectral Enhanced Images)

Plasma Actuators for Super/Hypersonic Flight

AIRFLOW OUTLET

WING

AIRFLOW + PLASMA

MAGNETIC FIELD AND PLASMA SOURCE COILS

ENGINE AIR INLET

AIRFLOW

Conceptual Scheme of Airframe Embedded Magnetized Plasma Actuator

Fig. 1 - Conceptual Scheme of the Airframe-Embedded Magnetized Plasma Actuator

MHD/Chemical Plasma Propulsion

NASA-Langley Seeded Plasma Accelerator for enhanced propulsion experiment (1965)

MHD/Chemical Plasma Propulsion

MHD Plasma Accelerator for wind tunnel experiment (USAF, 1999)

MHD Generator

MHD/Chemical Plasma Propulsion

Magnetic Nozzle

De Laval Nozzle

MHD Accelerator

Optimized SCRAMJET

General scheme of an MHD Augmented propulsion system

System study on the efficiency of an MHD Augmented Atmospheric Propulsion System

MHD/Chemical Plasma Propulsion

Scramjet-Driven Air Borne MHD Generator Concept (US Air Force)

MHD/Chemical Plasma Propulsion

Assembled Scramjet MHD Test Bed

Plasma-Spacecraft Interactions

Spacecraft Charging Hazard

the dielectric coating

Spacecraft Charging Hazard (II)

The ISS has large surfaces (MMOD shields) covered by a thin

(1.3 mm) anodized aluminum as a dielectric insulator

Voltages as low as 70 V have been found to produce arcing on
Long-term exposure of the dielectric surface to the space environment can produce local damages (due to micro- meteorites or debris) of the dielectric and enable arcing at even lower voltages

Spacecraft Plasma Hazard (III)

EVA space suits have a safety threshold of 40 V (Marshall Space Flight Center test showed arcing through the suit at 68 V with new fabric)
Beyond the 40 V value it is possible that a circuit close through the astronaut’s thorax cavity with a current in excess of 1 mA
This current limit is generally accepted as safety threshold to

prevent heart fibrillation.

Spacecraft Plasma Hazard (IV)

ISS Floating Potential Probe

FPP

the plasma contactor is a plasma source that establishes an electrically conducting path (the plasma) between the spacecraft ground and the ionosphere.

Plasma contactors are devices that allow to control

the maximum floating potential of a spacecraft by providing a discharge path to the ionosphere for the excess electrons

Essentially,

Plasma Contactors

The floating potential of the spacecraft

is then “clamped down” to safe values (in the order of -10 V for the current ISS implementation) ISS plasma contactors are Xenon sources (hollow-cathode design, maximum current of 4 A, much larger than the present requirements)

In steady-state conditions a plasma sheath is formed between the contactor plasma and the spacecraft conducting surface

For large values of the spacecraft floating potential the current in the sheath can be computed through the Child law and is independent on the spacecraft floating potential
Corrections to the Child law can be introduced for collisional sheaths: in this case there is a dependence of the current on the potential.
For example a (ion) plasma current of about 12 A can be sustained in a Hydrogen plasma with density of 1018 and temperature of 1 eV with a plasma radius of 5 cm.

Plasma Contactors

If transients occur (for example a sudden variation of the spacecraft potential at orbital sunrise) the sheath thickness adjust itself to new the value of the potential causing variations of the current that are also dependent on the potential. If the plasma contactor is effectively lowering the floating potential to small values (compared to the ionospheric plasma temperature) the sheath becomes much smaller (few Debye the equilibrium conditions lengths) and a calculation of according to the Bohm sheath criterion should be performed.

If a high-density plasma is produced near a conducting surface of a spacecraft in the Earth orbit an additional current path to the ionosphere will be established (in addition to the path represented by the interface between the ionospheric plasma and the spacecraft exposed conducting surfaces).

Plasma Contactors

is much higher

On the ISS, the charging due to the solar panels produces an electron excess on the station structure and brings it to a potential energy that is significantly larger than the thermal energy of the ionospheric plasma.
This is often expressed in less rigorous terms by saying that than the plasma

the “floating potential temperature”.

Plasma Contactors

Plasma Source

that

is: current discharges plasma electrons to the ionosphere

through the sheath supported by the ISS floating potential

* Plasmas

Main Thrust for Plasma Research: Fusion Energy
Aerospace Applications

Outline

Airfoils for Super/Hypersonic Flight
MHD/Chemical Plasma Propulsion
Plasma Contactors
Electric Propulsion

by the propellant-oxidizer reaction

only with a larger ejected mass flow.

propellant that needs to be stored aboard

Limitations of Chemical Rockets

Chemical rocket: exhaust ejection velocity intrinsically limited
Larger velocity increment of the spacecraft could be obtained
Mission practical

limitation: exceedingly large amount of

The Rocket Equation

Understanding the motion of a spacecraft

The Rocket Equation (II)

The rocket equation links the mass of exhausted propellant the relative exhaust velocity uex and the velocity

DM, increment of the spacecraft Dv:

For a given Dv, the larger uex , the smaller DM, and viceversa
A large DM requires the storage of a large amount of

propellant on board, reducing the useful payload

01expexvmMuDDthrough electro(magnetic) fields

Advanced (Electric) Propulsion

There is no intrinsic limitation (other than the relativistic one) to

the speed to which the propellant can be accelerated

Energy available on board is the only practical limitation

The Concept:

Definition - Electric propulsion: A way to accelerate a propellant

Advanced (Electric) Propulsion (II)

Understanding what’s behind it:

Tradeoff 1: more energy available, less propellant mass required
Tradeoff 2: more time allowed for a maneuver, less power

needed

than in conventional (chemical) rockets

Advanced (Electric) Propulsion (III)

Much less propellant consumption (much higher efficiency in the

Features:

High exhaust speed (i.e. high specific impulse), much greater

fuel utilization)

Continuous propulsion: apply a smaller thrust for a longer time
Mission flexibility (Interplanetary travel, defense)
Endurance (commercial satellites)

Electric Propulsion Concepts

Variety of designs to accelerate ions or plasmas
Most concepts utilize grids or electrodes: power and endurance

limitations * Ion Engine

Hall Thruster
RF Plasma Thrusters (ECR, VASIMR, Helicon Double Layer)
Magnetoplasma Dynamic (MPD) Thrusters
Plasmoid Accelerated Thrusters

Ion Engine

Scheme of a gridded ion engine with neutralization

Ion Engine

NASA’s Deep Space One Ion Engine

Ion Engine

NASA’s Evolutionary Xenon Thruster (NEXT) at NASA’s JPL

Hall Thruster

The Hall effect

Hall Thruster (II)

The Hall thruster scheme

Hall Thruster (III)

The Hall thruster: the Hall effect confines electrons

Hall Thruster (III)

High Voltage Hall Accelerator (HiVHAC) Thruster - Hall Thruster (NASA Glenn R.C.)

MagnetoPlasma Dynamic Thruster

The MPD thruster

Helicon Double Layer Thruster Experiment

Artists rendering of a Helicon Double Layer Thruster concept (Australian National University)

Helicon Double Layer Thruster Experiment

2005 Helicon Double Layer Thruster Experiment (European Space Agency, EPFL, Switzerland)

2003 Helicon Double Layer Thruster Experiment (Australian National University)

Plasmoid Thruster Experiment (PTX)

PTX Schematic (NASA MSFC/U. Alabama)

Plasmoid Thruster Experiment (PTX)

PTX Plasmoid Images with Coil Current

Electric Propulsion Applications

ISS

Commercial/Defense

Interplanetary Missions

ISS Electric Propulsion Boosting

ISS meeds drag compensation

Currently ISS is “reboosted” periodically
Presently Shuttle (or Soyuz) perform this operation
Very high cost: 9000 lbs/yr propellant at $5,000/lbs = 45M$/yr!

Future Perspectives: Fusion Propulsion

The Field Reversed Configuration is a plasma confinement scheme very appealing also for propulsion applications

Fusion Propulsion

FRC plasma simulated with the MHD-2 Fluid NIMROD code

Electric Power

FRC

Magnets

Fusion Propulsion

Plasma Accelerator

Magnetic Nozzle

Exhaust

Plasma and power production scheme for a FRC fusion (still to be demonstrated…) indirect propulsion rocket

Electric Power

FRC

Magnets

Fusion Propulsion

Magnetic Nozzle

Exhaust

Plasma and power production scheme for a FRC fusion (still to be demonstrated…) direct propulsion rocket

* The Field Reversed Configuration (FRC) is an attractive concept for plasma propulsion because its intrinsically high plasma beta and the formation of magnetically detached plasmoids.

FRC Direct Propulsion

Direct FRC fusion-propulsion schemes (that is, besides the basic concept of a reactor producing electricity to power a thruster) have been previously discussed (e.g. [1]), with the plasma exhaust accelerated directly from the fusion core or collected from the FRC scrape-off layer and channeled through a magnetic nozzle

Propulsion, Huntsville, AL, Nov. 2000 and General Atomics report GA- A23579, Dec. 2000

[1] M.J. Schaffer, Proc. NASA Advanced Propulsion Workshop in Fusion

FRC Fusion Plasma Thruster Concept

The plasma detachment in the nozzle is then induced in a

controlled way, through the formation of a sequence of FRC plasmoids

Confined plasma column

Plasma Generation

FRC Formation Coil

Fusion Product Energy Direct Converter

FRC Ignited Plasmoid

FRC Plasmoid

Confinement Coils

Short-term: Sub-critical FRC’s

The case of a sub-critical (without fusion yield) FRC is also interesting for the possibility of increasing the overall nozzle performance via a controlled detachment and of implementing plasmoid pre-acceleration schemes.

Long-term: FRC Fusion Propulsion

For an FRC plasmoid able to sustain fusion conditions,

the energy of the fusion products can be collected in the nozzle, while the plasmoid is leaving the rocket (ideally via direct conversion from neutron-free reactions) with transit time in the nozzle longer than the ignited FRC life time.

Only the fusion products that are escaping radially the detached plasma (plasmoid) are interacting with the rocket and are not expected to produce appreciable net back-thrust.

lifetime of the plasmoid.

Long-term: FRC Fusion Propulsion (II)

The fusion power can be collected in the nozzle during the
Assuming that the plasmoids are formed in a 1ms and have the lifetime of 100 ms and that they travel at 5∙104 m/s the direct conversion system should be 5 m long (if the fusion conditions are maintained for the lifetime of the FRC).
A D-T plasmoid with density of 1∙1020 and T=10 keV will

produce a power density of about 3MW/m3. For plasmoids of a 1 m3 volume, e.g., r=0.22 m, R=1 m, P=3 MW

The mass of one of these plasmoids will be: mpmd=2 ∙1020∙2.5∙1.67∙10-27=8.77∙10-7 kg
The thrust for 1 plasmoid per ms ejected at 5∙104 m/s will be

T=5∙104 (m/s)∙8.77∙10-7 kg/(1∙10∙10-3 s)=43 N and the specific impulse will be about 5000 s.

- Current Application Focus

MHD Augmented Propulsion (UHCL)
RF Magnetized Plasma Sources, Atmospheric Plasma Torches

Research at UHCL

(Propulsion, Re-entry plasma) (UHCL/JSC) Plasma Actuator/Airfoil for Hypersonic Flight (UHCL) FRC-based Electric Propulsion (Fusion/Propulsion) Lightning Stroke Simulation (JSC)

Magnetic Reconnection (UHCL)
Development 0-D Plasma-Neutral model

Some applications require neutrals:

1. Fluid (MHD) Plasma Simulation 2. Particle Simulation 3. Computer Science: Massively Parallel Processing

Theory

Simulation Studies

Experiments

Simulation

2. Continuity Equation:

Pre-Maxwell Equations:

MHD Plasma Simulation

Ohm’s Law (resistive MHD)
Momentum Equation
Energy Equation

, ppjEB,nntu,, ,,,,ptujBuu,,,,,TnTpQtuq,,,puBjE2. Continuity Equation:

Pre-Maxwell Equations:

MHD Plasma Simulation

Ohm’s Law (resistive MHD):
Momentum Equation:
Energy Equation:

0 , ppptmBEBj()0nntu ()ptuuujBu1nTTpQtuuq0,ppEuBjBBBMHD Plasma Simulation

Physical Model:

= me/mi is the mass ratio m0 and 0 are the permeability and permittivity of free space n is the number density is the mass density v is the center of mass velocity B is the magnetic flux density E is the electric field J is the current density p is the scalar pressure Q is the heat flux is the electrical resistivity P’=pI+P, I is the unit tensor P is the symmetric, traceless part of the stress tensor

Legenda

Magnetic Reconnection Leading to Detachment

Field line perturbed by the plasma current stretches and eventually reconnects producing a detached plasmoid (ring-like) structure

Reconnection Studies: Magnetic Nozzle Perturbation

NIMROD MHD Simulation: Step 450000 = 425 ms

FRC-based Plasma Thruster

The plasma detachment in the nozzle is induced in a controlled way, through the formation of a sequence of FRC plasmoids.

Plasma Accelerator

Accelerated Plasma

FRC Formation Coil

FRC Plasmoid

“Columbia” at NASA-Ames: 20 SGI® Altix™ 3700 superclusters, each with 512 Itaniunm processors = 10240 processors

Simulation Hardware

In-house Linux Clusters

MHD Accelerator

MHD Generator

Mass Flow Controller

Automatic RF Matching Networks

RF Generator

Argon

Building the UHCL Plasma Lab

Magnetic Nozzle Coils

Coil Power Supply

RF Plasma Torch

Mass Flow Controller

Argon

Building the UHCL Plasma Lab

Vacuum Chamber

Plasma Toroid Experiment

High-Vacuum Pump

Coil Power Supply

High-Voltage Power Supply and Capacitor Bank

Formation and Confinement Coils

The Field Reversed Configuration (FRC) is a well studied plasma confinement scheme that is very appealing also for propulsion applications

Fusion and Plasma Propulsion

A conceptual scheme for a FRC Rocket

Electric Power

FRC

Magnets

Fusion and Plasma Propulsion

Magnetic Nozzle

Exhaust

Plasma and power production scheme for a FRC fusion (still to be demonstrated…) direct propulsion rocket

A sequence of FRC plasmoids is formed from an accelerated plasma column

Confined plasma column

Plasma Generation

FRC Plasmoid Fusion-Propulsion Concept

Fusion Product Energy Direct Converter

FRC Formation and Acceleration

FRC Ignited Plasmoid

FRC Plasmoid

Confinement and Plasma Acceeration

APPENDIX A

- Examples:

The computer “particles” are elementary (at some level) constituents of a complex system

Galaxies

Plasmas

Particle Simulation

(Aggregates of) Electron, ions

Molecules, Atoms

Macromolecules

Particles

Stars

Materials, Fluids, Gases

Biological Systems

System

* A discretization grid is introduced to compute quantities like density, temperature, electromagnetic fields

Particle Simulation

Discretization of a 2D domain. In reality many particles per cell are typically considered

Basic Algorithm Summary

t=t+Dt

Initial particle loading

Compute interparticle forces

Particle Simulation

Solve particle equation of motion

t>tmax?

END

yes

Update particle positions and velocities

Massively Parallel Processing

Parallel Computing: many “chips” (processors) working on the same problem

Processor 0

at the same time

Processor 1

Processor 3

Processor 2

* The “parallelization” must not add significant overhead.

Massively Parallel Processing

Parallel Computing cannot defeat the causality principle: only operations

within the same time step can be performed simultaneously

Linear scaling: doubling the number of processors reduces computing time in half

Particle models can often be considered “embarassingly parallel” as their computational performances depend linearly on the number of particles
Present day massively parallel computers can run simulations in the 100

million particle range (fusion plasma applications)

efficient anymore…)

Massively Parallel Processing

~Past: access to NASA and NERSC supercomputers (not so
Present: Linux Cluster (in continuous evolution)
Future: waiting for availability of cheaper 64-bit clusters

APPENDIX B

NIMROD MHD SIMULATION:

Fluid Modeling of Plasma Flow in a Magnetic Nozzle

kinetic energy profiles

nozzle: quantitative picture

Effect of anisotropic conductivity on temperature and directed
Resistive (3D) MHD evolution of plasma profile in the magnetic

Fluid Modeling of Plasma Flow in a Magnetic Nozzle

Showing a case of plasma detachment (besides )
Reconnection in the detaching plasma
Electron temperature effects: two-fluid simulation
3D plasma exhaust stability analysis
Magnetic nozzle efficiency

The tool: NIMROD Fluid Simulation Code

Finite element formulation
Parallel code (supercomputers, Linux clusters)
NIMROD [3] DOE Multi-Institution Project
MHD and two-fluid (ions and electron temperature)
3D (r-z-j), nonlinear, time-implicit code
General geometries (toroidal, cylindrical), non-orthogonal

grid

[3] http://www.nimrodteam.org

2. Continuity Equation:

Pre-Maxwell Equations:

NIMROD Equations

Momentum Equation:
Energy Equation:

0 , tmBEBj()0nntu ()ptuuujBu1nTTpQtuuq//2ˆˆˆˆ:TvisnTQqbbIbbJVV5. Generalized Ohm’s law:

NIMROD Equations (II)

20 11 111 (1)(1) eipeIdealMHDResistiveMHDHallEffectDiamagneticEffectsElectronInertiaandNeoclassicalClosuresnenetEuBJJBJPPuJJueipmmPIΠBounded Plasma Flow: Density Evolution

NIMROD Movie Clip

Simulation of Plasmoid Formation in the Nozzle

NIMROD Simulation: density contours and field lines with induced translating plasmoid in a 10 m long magnetic nozzle

“Open” Plasma Flow: Density Evolution

NIMROD Movie Clip

t=6ms

Plasma Magnetic Field

|Bplasma| contours

De Laval Magnetic Nozzle NIMROD Simulation

t=0

t=0.9 ms

Mach # contours in t=0

Density contours

De Laval Magnetic Nozzle NIMROD Simulation

t=0

t=18 ns

t=170 ns

t=900 ns

t=660 ns

Time evolution of Mach # contours

boundary conditions

NIMROD Simulation: Next Steps

Fluid simulation with “strong” flows is not easy…

Work in progress on improved matrix solver and open-end

APPENDIX C

MHD Plasma Simulation

public domain (US Dept. of Energy):

Fluid, 3D code for magnetized plasma available in the
No development from scratch, upgrades only
Modeling 3D plasma plume dynamics in the magnetic field
Studying the plasma exhaust detaching from the nozzle:

efficiency.

Magnetic nozzle design optimization for the maximum

computing useful thrust

* The plasma currents in the nozzle: physical analysis and

Theory of Plasma Flow in Magnetic Nozzle

Perturbation of the external magnetic field: qualitative picture
Reconnection patterns and detachment: physical picture

estimates

Plasma Flow

Magnetic Nozzle

MHD Plasma Simulation

Model Geometry

MHD Plasma Simulation

* Diamagnetic current

Currents in the Exhaust Plasma

Grad-B current
B-Curvature current

2DpBBj2222122BLcvnqvrnmBRBcRBBBj222cfcnmvRBcRBjDiamagnetic Current: Physical Picture

Diamagnetic current produced by the pressure gradient

grad p

22[]BiBenkTkTpBBBBjMagnetic Nozzle Perturbation

B0r

Nozzle Field

B0z

Bcoil =B0

jplasma=jf

BT BTz

Bplasma

Plasma Field

Total Field

BTr

Magnetic Nozzle Perturbation: MHD Simulation

Log(density) contours

NIMROD MHD simulation: snapshot showing a plasma transient propagating while perturbing the magnetic nozzle field