Potential profiles have been measured on INS-e with an emissive probe and compared with theoretical stability predictions. So far there is good agreement between theory and experiment, but the stability limits have not yet been accessed experimentally

Munson, Carter P.

Nebel, Richard A.

Park, Jaeyoung

Rellergert, Wade G.

Sekora, M. D.

UNT Digital Library

Approved for public release; distribution is unlimited. Title: Author(s): Submitted to. Experimental and Theoretical Studies of Electrostatic Confinement Jaeyoung Park, Richard A. Nebel, J I Carter P. Munson, Wade. G. Rellergert, Yale Univeristy Mike D. Sekora, MIT APS/DPP 02 Meeting on Plasma Physics A Los Alamos N A T I O N A L  L A B O R A T O R Y  Los Alamos National Laboratory, an affirmative actiodequal opportunity employer, is operated by the University of California for the U.S. Department of Energy under contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the US. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the US. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. Form 836 (8/00) Experimental and Theeretical Studies of Electrostatic Cdnfinement J. Park, R. A: Nebel, C. P. Munson Wi G. Rellergert, M. Sekora Los Alamos National caboratory Los Alamos, New Mexico I 87545 Outline I. Electrostatic Basics 11. Motivation 111. Review of Periodically Oscillating Plasma Sphere physics IV. Potential "Show Stoppers" V. Equilibrium and Stability of Virtual Cathodes VI. Experiment VII. Spherically Convergent Ion Focus (SCIF) Systems VIII. INS as a neutron Source IX. Conclusions Electrostatic Basics 1. T - Vapplied (easy) A. B. C. Inexpensive machines give lots of neutrons Near-term applications as neutron sources Advanced fuels are easier than in conventional systems 11. %classical - 00 (not too bad) A. .B. Confine plasma in deep potential wells No cross-field diffusion size limit 111. Density limited by hDeff/a - 1 (difficult) A. Low density => Low power density B. Power density - l/r4, Power out - l / r  IV. Summary A. Small size, high voltage (difficult technology problem) B. Density enhancement scheme required 1. 2. Oscillating thermal plasma Focused ion plasma ( subject to Nevins problem) * * * * * Why IEC? Massively Modular Penning Trap Reactor Penning Trap Reactor Vessel Outflow +- Penning Trap FuelRods - (1 00s of cm sized sources) Coil J Plenum for electron sources, gas control and High voltage Pressure Vessel Mass Power Density for Modular Reactors is a paradigm shift from conventional systems. 2 3t Tl Pwa,, a2  F a  h b e  MPD = a ( 2 a t + t2) P High MPD (- LWR) can be achieved with conventional wall loads. Why can we do this with IECs? - Confinement doesn't depend on size - Power out - l /rtube Problem: Beam Systems have Trouble getting Q > 1. Power Scaling I. Poissonls Equation ne - V2+ - A+/a2 (note: here 11 a 11 is the rtube) 11. Average ion density - 10% electron density ni - .lne 111. Fusion power density IV. Total power P = 4/3na3p - l/a extractor dispenser cathode I Grid  V = +75 KV 1. 1-D Time and space separable solutions exist. 2. Solutions are stable. 3. Stable spectrum has an infinite number of discrete modes with accumulation point at o=O. 4. Density profile is Gaussian in radius, Maxwellian in velocity. 5. Profiles remain in 1.t.e. throughout oscillation (eliminates "Nevins Problem") Solutions likely to be attractors. 6.  2. 3. D. C. Barnes, R. A. Nebel, Physics of Plasmas 5,2498 (1998). R. A. Nebel, D. C. Barnes, Fusion Technology 38,28 (1998). POPS Ion Physics 293 , 4 inches r dispenser cathode Ion Phase Space Motion in a Harmonic Oscillator -. - - .  . . .  . . . .  . .  . .  t vx * :. . . .  . . .  D X . . .  * . .  . . .  t = O  (Particles at rest with small thermal velocity) -.:: I.:. .. .-I Distribution Functions Move as a Rigid Rotor. Density and Velocity Profiles Exchange Every 1/4 Period. Maxwellian velocity distribution requires Gaussian density profile Potential Show Stoppers High Voltage, Small Size - How bad is it? - Stability limits on Virtual Cathode (Electron Cloud). Electron Cloud Uniformity - Attractor * Energy Flow-through Issue How fast do the ions relax and thermalize? - Space Charge Neutralization During Ion Collapse Impurity Control Oscillation Phase Locking and Control Insulator Integrity Virtual Cathode Equilibrium and Stability Equilibrium Pressure balance and Poisson's equation lead to $oefdr) = $00eM(1- (r/a12) where po(r) = POO + eno($oefdr) - $ooeff) Stability Energy principle leads to sufficient condition for stability dS/d$oeff -= 0. (Rayleigh-Taylor criterion) where s=p/(men)Y is the entropy density. But for constant density dS/d$oefi = (dp/dr)/(d$o,ff/dr) = en0 > 0 which is always violated everywhere in the plasma. Dimensionless Linear Eigenvalue Equations @ " + 2/x@ ' - 1(1+1)/x2@ = 6n -Q2(AD/a)$ + Q,ff'X/3[-(A~/a)$' + @ '/6 + (Qeff'x/3)n] + r[(AD/a)2 + Q,ff2x2/6]Q2n = 0 The equations form a fourth order, self-adjoint system of equations. The only dependences are on AD/a, Oeff , r, and COpe . 2 2 10 ' 1  Y .1 .01 .OO Growth Rates Growth Rates vs. k l a  v- Qen 2 7  = -.5 YO .1 1 10 2 hD/a Growth rate versus Ada for various values of Q,R . * No window of absolute stability * Marginal points at Brillouin limit and hD/a - infinity. * ' y - 1 / (hD/a) for large hD/a (incompressible Rayleigh-Taylor limit). Stable Virtual Cathodes Do stable profiles exist that are sufficiently close to the desired harmonic oscillator potential that the POPS scheme will work?' Combine the marginally stable compressible Rayleigh-Taylor profile: d(p/nr)/dr = 0 with pressure balance and Poisson's equation and write in dimensionless form: where Y = rho, andvb = nb/nor. 1.06 1.04 n/nor 1.02 1.00 Mar gin a1 Stability 0.0 0.2 0.4 0.6 0.8 1 .o x=r/a Marginally stable density profile for hD/a = 6.2, a$/$ = .l% -14 -1 2 -1 0 -0 -6 -4 -2 0 1  a f f 2  Stability Diagram Kinetic Effects Compressible Rayleigh-Taylor + Electron-Electron Two-Stream * Approximations - Cold beam - Slab geometry * Dispersion relation 1 = op:[l/(~ + kVo)2 + 1/(0 - ~ V O ) ~ ]  * Marginal Limit * Conclusion: 1 5 (hD,ff/a),,it for two-stream stability * Does a critical value for hDeff/a exist? Fluid results (thermal electron distribution): Stable virtual cathodes exist which are "close enough" to the desired harmonic oscillator potential if: 1.2< hDeff/a. Kinetic results (self-colliding beam distribution): Stable virtual cathodes exist if: 1 < hDeff/a: We propose to find (hDeff/a)crit experimentally. Why is (hDeff/a)crit mportant? +vs. Radius T Virtual Cathode 2 1 Applied Vo I t ag e Radius L Virtual Cathode Stability Summary * POPS virtual cathodes violate a compressible Rayleigh-Taylor stability criterion for electrons. * Growth rates fall at large hDeff/a and near Brillouin limit, but no window of absolute stability exists in the fluid model. * Stable profiles that are "close enough" exist for hDeff/a 2 1.2 * Kinetic 2 stream limit suggests that a critical value of hDeff/a for stability exists and that this value is - 1. 2 * Since $applied - (hDeff/a)crit determining (hDeff/a)crit is critical to POPS performance. Experimental Program * Equilibrium and Stability of Virtual Cathodes. INS Device INS Device Configured for Virtual Cathode and POPS K2 (Emitter *2, 1 inches Shell (Grwunded) XG2 ( E x t r a c t o r  G 1 : (Outer Grid) 0 - 600V Langmuir Probe 0 Emissive Probe Used to Measure Plasma Potential Emissive probe for plasma potential measurement Made of thoriated tungsten (0.076 mm x 1 cm) in alumina tube (3.2 mm O.D.) Better suited than Langmuir probe due to electron beam Floating potential of hot probe N plasma potential (within 1-2 V) May disturb plasma: via ion loss to alumina tube - following results are taken from floating potential of hot probe 25 2 W 20 d) 13 .d E a 5  0 Y Current to emissive probe vs. heater current Heater current @ 1.1 A Floating potential 1 - 2 V lower than $ 0 10 20 30 40 50 Probe voltage (V) Radial Plasma Profile as a function of Gas Pressure Low Gas pressure - deep potential well (up to 60% of bias voltage) Increasing gas pressure - smaller well depth, radial asymmetry, bifurcation High Gas pressure - no well formation Middle, Outer and Extraction Grid @ 1OOV 100 80 60 40 20 0 -4 / 7 Outer Grid @ 1oov \ Middle Grid @ 1OOV I I I I I I I I I I I I .  I 1 I I -2 0 2 4 6 Radius (inch) Electron density profile from plasma potential Low pressure case - low ion density, compared to injected electrons due to low background ionization Ignoring ni, ne can be solved fr om Poisson equation (low ni verified later) ne profile from average of 4th order and 6th order polynomial fit of QP Off-peak radial density profile: stable profile from fluid dynamics standpoint Average electron density in the well - 3 . 3 ~ 1 0 ~  ~ m - ~  , consistent with electron density calculation from circulating current inside middle grid. Measured plasma potential and polynomial fitting Calculated electron density profile 70 - 9 .- Y 6o - Gas Pressure:lxlO- torr W Y E Middle, Outer, Extract0 a0 Grid @ lOOV cd 50 - E 3 - - 40 - a Middle Grid 30 I I I I I -0.5 0 0.5 1 1.5 2 2.5 Radius (inch) - c: E 0 0 \o I ---e-, avg. ~ i e  (4th and 6th) 4 t  1 -0.5 0 0.5 1 1.5 2 2.5 Radius (inch) Profile Results Experimental Observation: = .143 Theoretical Electron Density Profile at Marginal Limit Calculated electron density ppofile T- E 6  E! 0 * I -e- ne-2nd order ne-4thorder o ne-6thorder ---+--~~vg. ~ ( 4 t J i ~ n d 6 t h )  - - I  /" I -0.5 0 0.5 1 1.5 2 2 5  Experimental Electron Density Profile Radius (inch) Experimental Profile should be stable Bifurcation of Radial Plasma Potential Profile Two stable equilibria for radial plasma potential profile Deep well: well depth of 50-70 V @120 V bias (note the radial inhomogenity) No well: well depth of less than a few voltage No bifurcation: low grid voltage (e.g. < 5OV)or high grid voltage (e.g. > 120V) 160 140 120 100 80 60 40 20 0 Radial Potential Profile vs. Middle Grid Bias Outer and Extractor Grid at 100 V, Pressure - 3 ~ 1 0 - ~  torr Middle Grid @ 120 V --2 0 2 4 6 Radius (inch) Hysteresis and Fluctuation of Plasma Potential slow fluctuation - 100 Hz Typically observed in deep well phase but much smaller in no well phase. Slow time scale --> ion motion & ionization rate. Hysteresis of plasma potential @P Different hysteresis path for different rate of voltage sweep Fast process for well disappearance vs. slow process for well formation Important time scale - 0.1 - 10 ms Ion Particle Balance Model (OD) Ion source in the well = Ion loss out of the well Ion source: ionization of background neutrals (gas pressure dependent) - Sion = ne n, <0Ve> Vwell 3 0: ionization cross section, v,: electron velocity, Vwell: well volume Ion loss: loss to the probe structure + loss out of well due to random thermal motion and well anisotropy - Lion = 0.25*ni vi Aprobe + 0.5*ni vi Awell exp (-AV/Ti), vi: ion velocity, Aprobe: probe surface area (alumina tube), Awell: well surface area, AV: well depth Poission equation: 6 AV/a2 - q/Eo (ne-ni), a = well radius - 1.5 inch Well depth: function of bias voltage and electron injection Sion = Lion --> f(ni/ne,ne,Ti) = nn (after rearranging terms) Relevant numbers: - 0 - 1 ~ 1 0 - l ~  cm2for 40 - 100 eV , nn =3.5x1Ol0 ~ m - ~  x Pr (Pressure in - 'e - 4.2x107* (V,-AV/2)o.5, V,: bias voltage (1OOV) - AV N 7.8 *( 1- n,/n,) *ne (in lo6 ~ r n - ~ ) ,  ne - 5x lo6 ~ m - ~  (from measurement) - Aprobe = 6.3 cm2 (at the center), Vwell = 232 cm3, Awell = 182 cm2 torr) - vi - 4 . 9 ~ 1 0 ~ * ( A V + T ~ ) ~ . ~  Solutions from ion particle balance model Graphically solving f(ni/ne,ne,Ti) = n n Low pressure: one solution (deep well) Medium pressure: 3 solutions (2 stable, Scenario 1: well depth proportional to bias voltage (ne increase with bias, not limited by electron injection) 1 unstable), bifurcation between deep well and no well High pressure: one solution (no well) Consistent with experiments Ion particle balance-solver 5 . 8 ~  1 0-6 torr / I I 1 1 1 1 1  1 1 1 1 1 1 1 1 1 1 1  0.2 0.4 0.6 ,OS -3 1 n/n (n at5x10 cm ) i e  e Scenario 2: well depth limited by electron injections (ne = fixed) Experiments indicate #2 case --> need to enhance electron injection Difference in well depth model Ion temperaure = 0.25 eV , , I  I , ,  1 1 1 ~ 1 1 1 ~ l 1 1  Bias = 1OOV Bias = 50QV (n at 5x106 cm-3) Scenario 1. e Bias = 500V Scenario 2 n./n 0 0.2 0.4 0.6 0.8 1 i e  Comparison with Experiments Bifurcation Or 3 SOlUtiOnS are Seen at Middle current electron density Potential Well exist without ion 10SS to the probe (r=3-O inch, outside the well) center (assuming const. grid transparency) Bifurcation Seen by middle grid current dI/dv (middle grid) slow above 150V, Potential well disappears with increasing bias voltage --> electron density limited by injection electron density limited by injection Enhanced electron injection --> deeper potential well Plasma Potentid ys. Bias Voltage 300 100 Outer Grid @ IOOV 3 250 - Extractor Gnd @ lOOV E 80 I I I I I 3 C 200 B 8 150 50 0 Gas pressure N 4x1U6 torr I I I Bifurcation seen in middle grid current \ dI/dV slows limited by 1 " 0 50 100 150 200 250 300 0 100 200 300 400 Middle Grid Bias Voltage (V) Middle Grid Bias (V) INS Experiment Summary * Potential profiles have been measured with an emissive probe * Bifurcated equilibria have been observed (three different states) * Bifurcated equilibria can be understood qualitatively and quantitatively with a simple ionization model. * Wells as deep as 60% of the applied voltage have been observed. * Experimental density profiles are strongly peaked off-axis. * Even though the potential wells are much deeper than expected, theory predicts that the observed density profiles should be stable. * Stability limits of virtual cathode have not yet been tested. The Next Steps Flatten Density Profiles. - More focused electron beam from dispenser cathodes. Operate with deep well at higher voltages. - Pulsed discharges. - Ion removal techniques like POPS dumping? More electron density in the well. - Look for stability limit. Look at fluctuation data. Look for ion current resonant response at POPS frequency. INS as Neutron Source G3 (Cen t ra l  Cathode) -75 K V  Parameter Present IEC Target or Already Proven Neutron Yield ( d s )  1 os 10" D-T or 5x108 D-D Lifetime (hours) 500 10,000 Operation Pulsed Pulsed or steady state Nominal cost $k $1 OOk Same Power 1kW 25 kW Cutaway view of INS INS Exxleriment INS Device Near-Term Applications - Neutron source for "real-time" assay HEU detection Nuclear waste assay Landmine detection High explosive detection (Unexploded Ordnance) * * * * * Drug detection * Chemical and Biological Weapons - Higher gain applications * Neutron tomography (imaging for the above) * Isotope production Transmutation of waste * * Power production (POPS required) Nuclear Assay Applications * High Explosives Detection (UXO, Landmines, Chemical Weapbns Dispersant, "Suitcase Sniffers", Truck Bombs, etc.) H2 + H3 - He4 + n (14.1 MeV) (fusion reaction) N14 + n N15 + y (10.8 MeV) * Special Nuclear Materials Detection * Spent Fuel Assay H2 + H3 - He4 + n (14.1 MeV) (fusion reaction) U235 + n - f j I  + 3n (fission and neutron multiplication or delayed neutrons) H2 + H3 - He4 + n (14.1 MeV) (fusion reaction) U235 + n - f j I  + 3n (fission and neutron multiplication) Pu239 + n - f p  + 3n (fission and neutron multiplication) * Sarin Detection H2 + H3 +. He4 + n (14.1 MeV) (fusion reaction) P31 + n - P32 + y (7.93 MeV) FI9 + n + F20 + y (6.60 MeV) - S32 + e- (1.17 MeV) F20 - Ne2' + e- (5.40 MeV) Nuclear Assay Applications cont. * VX Jr Chlorine H2 + H3 - He4 + n (14.1 MeV) (fusion reaction) N14 + n - N” + y (10.8 MeV) P3’ + n + P32 + y (7.93 MeV) S32 + n - S33 + y (8.64 MeV) P32 - S32 +e- (1.17 MeV) H2 + H3 4 He4 + n (1’4.1 MeV) (fusion reaction) C13’ + n + C136 + y (7.97 MeV) Nuclear Assay Applications cont. * Mustardgas H2 + H3 - He4 + n (14.1 MeV) (fusion reaction) S32 + n - S33 + y (8.64 MeV) C13’ + n - C136 + y (7.97 MeV) * Cyanide H2 + H3 - He4 + n (14.1 MeV) (fusion reaction) N14 + n - N” + y (10.8 MeV) * Biological Weapons (Anthrax, Small Pox, etc.) H2 + H3 - He4 + n (14.1 MeV) (fusion reaction) n + processing chemicals - processing chemicals + y Conclusions Potential profiles have been measured on INS-e with an emissive probe and compared with theoretical stability predictions. So far there is good agreement between theory and experiment, but the stability limits have not yet been accessed experimentally. Next Steps - Flatter Density Profiles. - Increase Voltage Operating Window. - Look for stability limit. - Look at fluctuation data. - Look for ion current resonant response at POPS frequency. 0 Build a lx10l1 Ion-based D-T Source. 

Experimental and theoretical studies of electrostatic confinement

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Experimental and theoretical studies of electrostatic confinement

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