Polywell Fusion: Electrostatic Fusion in a Magnetic Cusp

Summary

This presentation delivered by Jaeyoung Park of EMC2 at the 2014 Fusion Power Associates Meeting outlines the experimental confirmation of enhanced electron confinement in a high-beta magnetic cusp (Wiffle-Ball configuration). It details the historical theory dating back to Harold Grad and Robert Bussard, presents experimental diagnostics and Bremsstrahlung x-ray measurement results validating the high-beta cusp confinement enhancement, and proposes the next proof-of-principle phase toward Polywell fusion.

Page 1: Title Slide

Polywell Fusion Electrostatic Fusion in a Magnetic Cusp

Jaeyoung Park Energy Matter Conversion Corporation (EMC2) Fusion Power Associates Meeting (December 17, 2014) Support from US Navy Contract: N68936-09-C-0125 Energy Matter Conversion Corporation (EMC2) 1

Page 2: Contributions from EMC2 Personnel

Contributions from EMC2 Personnel

4 Scientists, 5 Engineers/Technicians, 2 Support

Mike Skillicorn: Design, construction and maintenance of WB-8 device Paul Sieck: WB-8 operation, control and safety system, and DAQ Dustin Offermann: Plasma diagnostics – Spectroscopy, lasers and x-ray Eric Alderson: Plasma diagnostics – Probes and particle diagnostics Mike Wray: Vacuum and gas handling system and lab Management Noli Casama: Electrical power system Kevin Davis: Microwave system and HV pulse power operation Andy Sanchez: Operation Support and Numerical Simulation Grace Samodal: Business/Operations Management Yoko Corniff: Accounting and HR Jaeyoung Park: Lead the WB-8 project

EMC2 works closely with Dr. Nicholas A. Krall on Polywell theory

Page 3: Contributors to the Polywell Fusion Concept

Contributors to the Polywell Fusion Concept

Philo Farnsworth: Electric fusion & inventor of television
Harold Grad: MHD theory and Cusp confinement
James Tuck: Picket Fence, Elmore-Tuck-Watson virtual cathode, & Explosive focus for A-bomb
Robert Bussard: Polywell Fusion, Nuclear Rocket, Bussard Ramjet

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Page 4: Polywell Fusion Principle

Polywell Fusion Principle

Combines two good ideas in fusion research: Bussard (1985) a) Electrostatic fusion: High energy electron beams form a potential well, which accelerates and confines ions. b) High β magnetic cusp: High energy electron confinement in high β cusp: Bussard termed this as “wiffle-ball” (WB).

Electrostatic fusion provides:

Ion heating
Ion confinement for high β cusp

High β cusp provides:

High energy electron confinement for electrostatic fusion

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Page 5: Polywell Cusp Magnetic Fields

Polywell Cusp Magnetic Fields

6 coil Polywell cusp magnetic field lines
Electron beam injection along the cusp openings

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Page 6: Potential Well by e-beam Injection (1995)

Potential Well by e-beam Injection (1995) at low plasma density

[Charts and excerpts from Krall et al., Physics of Plasmas, 1995 detailing HEPS Experiment and Potential Well Formation via 1 e-gun @ 8 kV, 3 Amps]

However, the potential well decayed away with increase in plasma density above 1x10^9 cm^-3, which was contributed to the insufficient confinement of fast electrons inside the Polywell cusp field (Krall et al, Physics of Plasmas, 1995)

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Page 7: Progression of EMC2 Polywell Devices

Progression of EMC2 Polywell Devices

[Images showing WB-2, WB-4, WB-5, WB-6, WB-7, WB-8]

Since 1994, EMC2 had built and operated successive test devices from Wiffle-Ball-1 (WB-1) to WB-8 to demonstrate confinement of high energy electrons in a magnetic cusp.

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Page 8: Motivation of Magnetic Cusp

Motivation of Magnetic Cusp

From “Project Sherwood: The U. S. Program in Controlled Fusion” by Amasa Bishop (1958). FIG. 19-2. CHRONOLOGY OF THE SHERWOOD PROGRAM, showing methods of plasma confinement in experiments to date (Cusped Geometry highlighted).

Magnetic cusp was introduced to magnetic fusion program for plasma stability and high beta (β=1) operation.

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Page 9: Grad’s High Beta Cusp Conjecture

Grad’s High Beta Cusp Conjecture

Low β:

Finite B-field (center)
Weak diamagnetism
Poor confinement

High β:

Zero B-field (center)
Strong diamagnetism
Sufficient confinement for net power reactor

• Between 1955-1958, NYU group led by Grad investigated the case of plasma confinement in a high β magnetic cusp. • In Grad’s view, a boundary between plasma and magnetic fields are very different for low β and high β case. • For high β cusp, he envisioned “a sharp transition layer to exist between plasma and B-fields, while diamagnetic effect results in a field free central region” • Plasma particles will undergo specular reflection at the boundary except for the particle moving almost exactly in the direction of the cusp -> the plasma loss rate will be greatly reduced and have gyro-radius scaling.

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Page 10: Plasma Confinement in Cusp at High β

Plasma Confinement in Cusp at High β

In high β cusp, a sharp transition layer exists between plasma and B-fields. Plasma particles will undergo specular reflection at the boundary except for the particle moving almost exactly in the direction of the cusp. The loss rate will have gyro-radius scaling.

(Berkowitz et al 1958 paper “Cusped geometries”)

Theoretically conjectured: Loss current per cusp by Grad and NYU team: I_{e,i} / e = (π / 9) * n_{e,i} * v_{e,i} * π * (r_{e,i}^{gyro})^2

-> 0.5s confinement time for 100 keV electron with 7 T, 1m radius, 6 coil cusp -> favorable for a net power device.

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Page 11: History of Cusp Confinement Efforts

History of Cusp Confinement Efforts

• Grad’s confinement enhancement conjecture made the cusp approach to be promising for a net power fusion reactor. • For the next 20 years, detailed experiments were conducted on ~20 different devices and ~200 papers were published related to the cusp confinement as a result. Two excellent review articles by Spalding (1971) and Haines (1977). • However, most efforts on cusp confinement stopped by 1980 due to a lack of progress.

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Page 12: High Beta Cusp Experiments in 1960s using plasma injection

High Beta Cusp Experiments in 1960s using plasma injection

TABLE I: Typical Injection—Cusp Experiments Summary of historical experiments using single-pulse coaxial guns, conical Z-pinch guns, theta-pinch guns, and titanium guns across various confinement geometries and quoted beta values.

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Page 13: Cont. High Beta Cusp Experiments in 1960s using plasma compression

Cont. High Beta Cusp Experiments in 1960s using plasma compression

TABLE II: Recent Compression—Cusp Experiments From review article by I. Spalding, “Cusp Containment” In Advances in Plasma Physics. (A. Simon, W. B. Thompson, Eds., Wiley, New York, 1971) Summary of experiments using adiabatic spindle cusp, shock preheat, linear theta-cusp, and toroidal hexapole.

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Page 14: Recent Experiments at EMC2 (EMC2 San Diego Facility)

Recent Experiments at EMC2 (EMC2 San Diego Facility)

[Photographs showing the WB-8 Device and the High β cusp Test Device in the laboratory facility]

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Page 15: EMC2 Experimental Plan

EMC2 Experimental Plan

Plasma injection to the cusp

Use high power arc (solid target) plasma injectors

Verify high β plasma formation in the cusp

Measurements on plasma density, magnetic flux and electron temperature

High energy electron injection to high β cusp

LaB6 based electron beam injector, used as fast test particles.

Confinement measurement of high energy electrons in the cusp

Time resolved hard x-ray intensity from bremsstrahlung

Bulk (cold & dense) plasma from arc injectors provides plasma pressure (high β) to modify cusp B-fields, while the confinement property is measured for high energy electrons in the cusp.

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Page 16: First ever confirmation of high β cusp confinement enhancement (October 23, 2013)

First ever confirmation of high β cusp confinement enhancement (October 23, 2013)

High β shot 15610:

High β Phase marked around 10-20 µs with peak X-ray face and corner cusp chord signals coinciding with ΔB flux exclusion and peak bulk electron density.
X-ray from impurities (e.g. W) occurs later (40-60 µs).
Diagnostics include 1/2 Arc Input Power, Hα line intensity, and CII line intensity.

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Page 17: Cusp confinement vs. Injection input power

Cusp confinement vs. Injection input power

B-field at 2.7 kG:

Compared shot 15631 @ 220 MW, shot 15650 @ 340 MW, shot 15630 @ 450 MW, shot 15640 @ 700 MW.
Graphs showing X-ray intensity / I_e injection (a.u.), Flux exclusion (mWb), and Bulk electron density (cm^-3) over time.

Cusp confinement enhancement requires sufficiently high β plasma condition.

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Page 18: Cusp confinement vs. initial B-fields

Cusp confinement vs. initial B-fields

Input power at 700 MW:

Compared shot 15621 @ B=0, shot 15677 @ B=0.6 kG, shot 15640 @ B=2.7 kG.
Graphs of X-ray intensity / Electron current, Flux exclusion, and Bulk electron density vs. time.

No confinement enhancement at B=0 but we need to do more to understand B-field effects.

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Page 19: Our Findings on High β Cusp Confinement

Our Findings on High β Cusp Confinement

Increase in X-ray signal:

Coincides with high β plasma state in the cusp
Only observed when there is sufficient flux exclusion or plasma injection reaches a threshold
Peak increase is 10-20x or more compared to low β state
Exhibits asymmetrical time behavior: gradual increase followed by rapid decrease
Clearly separated from W impurities injection in time domain

We believe our x-ray measurements unambiguously validate the enhanced electron confinement in a high β cusp compared to a low β cusp. (Technical paper submitted to Physical Review X and preprint available on arXiv:1406.0133 (2014))

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Page 20: A Path to Polywell Fusion

A Path to Polywell Fusion

High β cusp (Confinement of energetic electrons) - Proven in 2013
Electrostatic fusion (Potential well for energetic ions) - Proven in 1995

-> Polywell: High β cusp + Electrostatic fusion at the same time

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Page 21: Merits of Polywell Fusion Reactor

Merits of Polywell Fusion Reactor

Scientific merits:

MHD stability
High β operation
Electrostatic heating of ions
No helium ash issue

Engineering merits:

Compact size
Heating by electron beam injection
Natural divertor
Modular, non-interlocking coils
Remote first wall

Polywell fusion may offer a low cost and rapid development path.

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Page 22: Movie of Polywell Fusion Reactor Assembly

Movie of Polywell Fusion Reactor Assembly

[Illustrations of Polywell fusion reactor chamber and coil assembly]

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Page 23: Next Phase: Last Part of Proof-of-Principle

Next Phase: Last Part of Proof-of-Principle

Sustained high β operation (~ 5 ms)
Demonstration of ion heating (>10 kV) by e-beam injection
Verify Grad’s cusp scaling

3 year, $25-30M program to complete proof-of-principle. Success will be defined by 1) high energy electron confinement within a factor of 10 from Grad’s conjecture and 2) minimum 30% ion heating efficiency via e-beam.

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Page 24: Teller’s Comment on Beta

Teller’s Comment on Beta

“The qualitative properties of the plasma depend on the ratio of pressures in the plasma and the magnetic field. The former is the plasma pressure p, the latter B^2/8π. The ratio of the two quantities 8πp/B^2 is known as β. In general, the plasma behavior is most simple for low-β values and most interesting for high-β values.” — Teller, page 13-14, “Fusion, Volume 1, Part A: Magnetic Confinement”, edited by Edward Teller, 1981

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Page 25: Supplemental Slides

Supplemental Slides

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Page 26: Electrostatic Fusion

Electrostatic Fusion Contributions from Farnsworth, Hirsch, Elmore, Tuck, Watson and others

Operating principles (virtual cathode type): • e-beam (or grid) accelerates electrons into center • Injected electrons form potential well • Potential well accelerates/confines ions • Energetic ions generate fusion near the center

Attributes: • Excels in generating energetic ions with good confinement • But loss of high energy electrons is too large

Deep negative potential well (1) accelerates and traps positive ions (2) until they generate fusion reactions. Net power generation is unlikely (present efficiency: 1-10x10^-6)

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Page 27: Question on Plasma Stability

Question on Plasma Stability

Reference: “Project Sherwood: The U. S. Program in Controlled Fusion” by Bishop (1958). • Question on Plasma Stability by Teller in 1954

“Attempts to contain a plasma as somewhat similar to contain jello using rubber bands”
Basis of interchange instability (plasma version of Rayleigh Taylor instability) and idea of “good curvature” vs. “bad curvature”

From Principles of Plasma Physics, Krall & Trivelpiece (1973) Stronger instability shown in an outer part of torus “Tokamak ballooning mode instability” from General Atomics Gyrokinetic simulation.

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Page 28: Experimental Setup for high β cusp confinement

Experimental Setup for high β cusp confinement

Chamber size: 45 cm cube, Coil major radius: 6.9 cm
Distance between two coils: 21.6 cm, B-field at cusp (near coil center) 0.6 – 2.7 kG
Components: LaB6 Electron Gun (7 keV, 1 – 3 A), Plasma Gun (300 MW solid arc), X-ray diode (2 keV x-rays and up, corner and face views)

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Page 29: Experimental Setup (continued)

Experimental Setup (continued)

Laser Interferometer (532 nm, 10^15 - 10^17 per cc)
Magnetic Flux Loops
Photodiodes and Spectrometer (Filtered for Hα and C I-II, High resolution spectrometer, fiber coupled)

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Page 30: Solid arc plasma injector

Solid arc plasma injector

Plasma injection by co-axial guns (j x B) using solid fuel:

Ignitron based pulse power system (40 µF cap holds 3 kJ at 12kV)
~100 kA arc current -> ~300 MW peak power and ~7 µs pulse
β=1 @ 2.5 kG: 1.5x10^16 cm^-3 at 10 eV or 100J in a 10 cm radius sphere
Solid arc using polypropylene film, 2 mm A-K gap

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Page 31: High β plasma formation (two plasma guns)

High β plasma formation (two plasma guns)

Plasma density on the order of 10^16 cm^-3 from Stark broadening of Hα line
Laser interferometer provides single shot line integrated density variation in time
Electron temperature is estimated ~ 10 eV from C II and C III emission
Hα, C II line by photodiode and visible spectra by gated CCD is used to monitor T_e variation in time

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Page 32: High energy electron beam produces hard x-rays

High energy electron beam produces hard x-rays

Process:

E-gun injects Beam Electrons (7 keV)
Beam electron confinement by Cusp magnetic fields
Collisions with bulk plasma create hard x-rays (E > 2 keV) via Bremsstrahlung

Transit time: ~7 ns for 7 keV electron for 22 cm transit Expected confinement time: ~45 ns for low β and ~18 µs for high β (x400 increase)

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Page 33: Bremsstrahlung x-ray emission from interaction between beam electrons and plasma

Bremsstrahlung x-ray emission from interaction between beam electrons and plasma

Bremsstrahlung radiation from e-beam interaction with plasma ions: e + ion -> e + ion + hν P_{Br} ∝ n_e^{beam} * E_{beam}^{1/2} * n_{ion} * Z_{eff}^2

Bremsstrahlung x-ray intensity -> Direct measurement of beam e-density inside Cusp

Careful measurement is required to eliminate spurious radiation from impurities, vacuum wall, coil surfaces, and characteristic line emission.

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Page 34: X-ray collecting optics to eliminate unwanted signals

X-ray collecting optics to eliminate unwanted signals

X-ray Diode and Collimator Assembly:

Silicon Diode Detector
Kapton-Black Film: Blocks plasma, blocks soft x-rays, blocks visible light
Magnetic Yoke: Blocks beam electrons with B-field
Collimator Tube: Limits view to plasma, plastic material minimizes x-ray production inside tube

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Page 35: Hard x-ray filter

Hard x-ray filter

25 µm thick light tight Kapton filter (works as vacuum interface) Filter has sharp cutoff at ~2 keV photon energy: -> blocks any characteristic x-ray emission from light elements up to 14Si and 15P -> blocks UV-visible light from plasmas -> blocks charged particles from reaching the detector

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Page 36: Confirmation of X-ray filter vs. beam energy

Confirmation of X-ray filter vs. beam energy

• X-ray was generated by electron beam on Stainless Steel target • 25 µm thick Kapton filter works well to eliminate X-ray photons below 2 keV [Graph of X-ray signal vs. Electron beam voltage (kV)]

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Page 37: Spatial collimation of x-ray detectors

Spatial collimation of x-ray detectors

• Collimation is designed to eliminate direct line-of-sight view of metal surfaces • In addition, opposite sides of the chamber wall are covered using Kapton film and quartz window • Both chords (Face cusp chord & Corner cusp chord) allow good volume averaging of x-ray emission from core plasmas

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Page 38: Confirmation of X-ray collimation

Confirmation of X-ray collimation

Image plate (x-ray film) exposure at the face cusp detector location shows uniform exposure and no sign of spatial structure from coils & walls (10 mTorr N2 gas target, 20 ms exposure with 4A@7 kV e-beam, B-field at 1.4 kG)
e-beam into vacuum magnetic field (no plasma) generates no x-ray response from the diode detector
Indication of well collimated x-ray optics

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Page 39: Reproducibility of high β cusp confinement

Reproducibility of high β cusp confinement

6 consecutive shots with ~ 200 J of injected plasma energy at 2.7 kG B-fields -> Estimated cusp beta ~ 0.7 from line averaged density at T_e ~ 10 eV All six shots (shots 15635 - 15640) show distinctive high β phase -> good reproducibility

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Page 40: Time averaged plasma images

Time averaged plasma images

[Photographs of plasma emissions for Shots 15635, 15636, 15637, 15638, 15639, 15640] High β cusp formation: intense plasma in the core region

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Page 41: Time resolved spectroscopy on W-impurity

Time resolved spectroscopy on W-impurity

• Line emission intensities from main ion species (H and C) decay early • Despite plasma density decay (& cooling of plasma), Tungsten line intensities peak later in time and decay slowly —> indicates gradual build up of Tungsten impurity. —> x-ray peak late in the shot (40-50 µs) is from e-beam interaction with Tungsten [Photograph of Tungsten cathode after 200 shots]

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Page 42: Time resolved spectroscopy for impurity transport

Time resolved spectroscopy for impurity transport

During the high β phase, plasma emission shows strong C+ lines & presence of W+ lines (Note that avg. n_e ~ 1.5x10^16 cm^-3 and T_e ~ 10 eV during this period) Visible emission spectrum between 12 µs and 20 µs

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Page 43: Time resolved spectroscopy (cont.)

Time resolved spectroscopy (cont.)

At later time, plasma emission is dominated by W neutral lines, while C+ and W+ lines disappear (Note that avg. n_e ~ 0.2x10^16 cm^-3 and T_e < 10 eV) Visible emission spectrum between 42 µs and 50 µs

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Page 44: Estimate of High β Confinement Time

Estimate of High β Confinement Time

Theoretical model to estimate high β confinement time vs. Experimental results (Shot 15640)
Note the shape of x-ray intensity profile: a gradual rise and a rapid drop (Δt ~ 5 µs)
From time response of x-ray signal -> τ > 2.5 µs (2x τ ~ x-ray signal rise time)
2.5 µs is about ~ 50 times better than low β cusp confinement time
The observed confinement enhancement is very significant and compares well with the theoretically predicted high β cusp confinement time by Grad and his team

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Page 45: Unresolved issues on high β cusp

Unresolved issues on high β cusp

Decay of good confinement phase

Decay mechanism: plasma loss/plasma cooling or magnetic field diffusion or something else
How to extend high β state and prevent the decay

Topological information on cusp magnetic fields during high β state

Thickness of transition layer
Magnetic field lines near the cusp openings

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