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 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 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 Energy Matter Conversion Corporation (EMC2) 3 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 Energy Matter Conversion Corporation (EMC2) 4 Polywell Cusp Magnetic Fields - 6 coil Polywell cusp magnetic field lines - Electron beam injection along the cusp openings Energy Matter Conversion Corporation (EMC2) 5 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) Energy Matter Conversion Corporation (EMC2) 6 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. Energy Matter Conversion Corporation (EMC2) 7 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. Energy Matter Conversion Corporation (EMC2) 8 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. Energy Matter Conversion Corporation (EMC2) 9 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. Energy Matter Conversion Corporation (EMC2) 10 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. Energy Matter Conversion Corporation (EMC2) 11 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. Energy Matter Conversion Corporation (EMC2) 12 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. Energy Matter Conversion Corporation (EMC2) 13 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] Energy Matter Conversion Corporation (EMC2) 14 EMC2 Experimental Plan 1. Plasma injection to the cusp - Use high power arc (solid target) plasma injectors 2. Verify high β plasma formation in the cusp - Measurements on plasma density, magnetic flux and electron temperature 3. High energy electron injection to high β cusp - LaB6 based electron beam injector, used as fast test particles. 4. 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. Energy Matter Conversion Corporation (EMC2) 15 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. Energy Matter Conversion Corporation (EMC2) 16 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. Energy Matter Conversion Corporation (EMC2) 17 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. Energy Matter Conversion Corporation (EMC2) 18 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)) Energy Matter Conversion Corporation (EMC2) 19 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 Energy Matter Conversion Corporation (EMC2) 20 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. Energy Matter Conversion Corporation (EMC2) 21 Movie of Polywell Fusion Reactor Assembly [Illustrations of Polywell fusion reactor chamber and coil assembly] Energy Matter Conversion Corporation (EMC2) 22 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. Energy Matter Conversion Corporation (EMC2) 23 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 Energy Matter Conversion Corporation (EMC2) 24 Supplemental Slides Energy Matter Conversion Corporation (EMC2) 25 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) Energy Matter Conversion Corporation (EMC2) 26 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. Energy Matter Conversion Corporation (EMC2) 27 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) Energy Matter Conversion Corporation (EMC2) 28 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) Energy Matter Conversion Corporation (EMC2) 29 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 Energy Matter Conversion Corporation (EMC2) 30 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 Energy Matter Conversion Corporation (EMC2) 31 High energy electron beam produces hard x-rays Process: 1. E-gun injects Beam Electrons (7 keV) 2. Beam electron confinement by Cusp magnetic fields 3. 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) Energy Matter Conversion Corporation (EMC2) 32 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. Energy Matter Conversion Corporation (EMC2) 33 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 Energy Matter Conversion Corporation (EMC2) 34 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 Energy Matter Conversion Corporation (EMC2) 35 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)] Energy Matter Conversion Corporation (EMC2) 36 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 Energy Matter Conversion Corporation (EMC2) 37 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 Energy Matter Conversion Corporation (EMC2) 38 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 Energy Matter Conversion Corporation (EMC2) 39 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 Energy Matter Conversion Corporation (EMC2) 40 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] Energy Matter Conversion Corporation (EMC2) 41 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 Energy Matter Conversion Corporation (EMC2) 42 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 Energy Matter Conversion Corporation (EMC2) 43 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 Energy Matter Conversion Corporation (EMC2) 44 Unresolved issues on high β cusp 1. 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 2. Topological information on cusp magnetic fields during high β state - Thickness of transition layer - Magnetic field lines near the cusp openings Energy Matter Conversion Corporation (EMC2) 45