Increased Upstream Ionization Due to Spontaneous Formation of a Double Layer in an Expanding Plasma

Transcription

1 Increased Upstream Ionization Due to Spontaneous Formation of a Double Layer in an Expanding Plasma Earl E. Scime* November, 2009 APS Division of Plasma Physics Meeting * with Costel Biloiu, Ioana Biloiu, Rod Boswell, Jerry Carr, Saikat Chakraborty Thakur, Christine Charles, Sam Cohen, Justin Ellis, Matt Galante, Alex Hansen, Zane Harvey, Saeid Houshmandyar, Amy Keesee, Dustin McCarren, Albert Meige, Steve Przybysz, Stephanie Sears, and Xuan Sun

2 HIGHLIGHTS Double layers form spontaneously in expanding, low pressure, high density plasmas Double layers require some tens of milliseconds to form in a pulsed discharge Under carefully controlled conditions, a theoretical model which argues that double layers form as a means of adjusting for differing upstream and downstream diffusive loss rates has been verified Strong double layer formation suppressed by growth of beam driven instabilities in pulsed plasmas.

3 OUTLINE Double layer fundamentals Spontaneous double layer discovery and comparison to Monte Carlo particle-in-cell model Tomographic and time-resolved double layer LIF measurements Helicon antenna frequency threshold for double layer formation and relation to model predictions Evidence for beam driven instability suppression of double layer for low antenna frequencies

4 GEOMETRY OF A STATIC DOUBLE LAYER (DL) Scale length ~ 10 s of Debye lengths (shielding distances) quasi-neutrality is violated! accelerated ions L.P. Block, Astrophysics and Space Science (1978)

5 DOUBLE LAYER CREATION IN LABORATORY EXPERIMENTS By mixing two different plasmas together Triple plasma device (magnetic field free) Current driven plasmas Q-Machines, ion beams into target plasmas, currents induced during reconnection Leading edge of a pulsed plasma Pulsed cathodes, pulsed electron beams Expanding, current-free plasmas with strong density gradient due to magnetic field expansion or gettering of electrons (l mfp > density gradient scale length) Chi-Kung, MNX, HELIX, ECR sources Sheath forms due to potential difference Current or instability driven Expansion speed exceeds sound speed Formation mechanism upstream ionization balance [Lieberman et al., 2006], sheath instability [Chen, 2006], boundary conditions [Meige et al., 2007]?

6 Plasma Potential PLASMA VELOCITY DISTRIBUTIONS INDICATE PRESENCE OF DL B ions electrons accelerated electrons ions electrons (V e > V te so current or beam required) weak double layer e 2-5kT e grounded chamber wall A trapped and a passing or beam electron (ion) population appear upstream (downstream) of the double layer. Typically an electron beam or drift is required to maintain the static, field aligned potential drop. However, current free double layers have been found localized to regions of strong magnetic field gradients [Hatakeyama et al., 1983]. Lieberman s recent current-free model argues for a 5 th, reflected electron, species.

7 EXAMPLE OF MAGNETOSPHERIC DL TRAPPED AND PASSING IONS Accelerated ions Sheath Aurora: FAST measurements C. Cattell et al., J. Geophys. Res. 107, 1238 (2002). Trapped ions Ion flux integrated over all pitch angles versus time for an earthward flowing ion beam.

8 Plasma potential (V) HISTORY: CHARLES AND BOSWELL [APL, 2003] - DOUBLE LAYER POTENTIAL STRUCTURE AND ION BEAM IN EXPANDING HELICON SOURCE PLASMA Beam V ~ 2C s DV p double layer from RFEA probe

9 ION BEAMS OBSERVED VIA PARALLEL LASER INDUCED FLUORESCENCE IN MNX [PHYS. PLASMAS, 2003] Background ions Ion beam ~ 9 km/s LIF nm 4s 4 P 3/2 4p 4 D 5/ nm 3d 4 F 7/2 Energy Analyzer When (RFEA) Zeeman shift in weakening field balances Doppler shift of accelerating ions, measured state asymmetry gives absolute measure of ion collisionality mean free path ~ gradient scale length

10 MONTE-CARLO -PIC SIMULATION SUGGESTS DENSITY GRADIENT TRIGGERS DL FORMATION Common geometry for all helicon source experiments reporting DLs A spatially dependent loss rate models the divergent magnetic field [Meige et al. Phys. Plasmas (2005)]. DL spontaneously forms when the loss rate exceeds a critical value.

11 IN MC-PIC, ION BEAM FORMS AT EXPANSION POINT, TWO ION POPULATIONS DOWNSTREAM OF DL sheath beam ~ 5 km/s double layer Joint ANU-France Monte Carlo, particle-in-cell simulation

12 FULL DL STRUCTURE, INCLUDING LONG PRE-SHEATH REGION, MEASURED IN HELIX. EXCELLENT AGREEMENT WITH MC-PIC MODEL [Sun et al., PRL 2005] The plasma potential measurements are consistent with the LIF ion energy measurements. The plasma potential tracks the magnetic field strength - decreasing along z. The pre-sheath and sheath are clearly visible and large enough for detailed study. pre-sheath sheath

13 f(v) IONS ACCELERATED TO ~ 10 KM/S DOWNSTREAM OF DL weak double layer as E Beam ~ 3kT e Ion Velocity (m/s) Position (cm)

14 LIF TOMOGRAPHIC STUDIES IDENTIFY MIRROR RATIO THRESHOLD FOR DL FORMATION

15 OPEN QUESTIONS Phenomenon could be used for plasma propulsion (ion beams without grids, filaments, etc.) - do double layers form in pulsed, expanding helicon discharges? Clear low pressure threshold for double layer formation - what is the physical mechanism? Can any strength double layer be created, or is there a limit? Do different mass ions fall through the double layer at the same speed or at the same energy? Does the ion beam detach from the magnetic nozzle?

16 TIME RESOLVED LIF DEVELOPED TO INVESTIGATE DL FORMATION PHASE ANU experiments indicate some DL formation within 100 ms (RFEA measurements difficult to quantify). Stenzel experiments in supersonically expanding plasmas indicate DL forms within a few ms (just an ambipolar field effect?). In HELIX, the DL forms within a few ms, but ion beam energy continues to increase until ~ 100 ms into discharge pulse. This measurement is in the DL and once the DL forms, the background ions are unable to reach the measurement location - so only one population is observed. ion beam Ion Velocity (arb)

17 THE DL TYPICALLY REQUIRES 10 S OF MS NO SHORT PULSE ROCKETS? More detailed study with 1 ms time resolution: the LIF-determined argon ion velocity distribution function during a 100 ms plasma pulse surface plot showing fast (~ 7.1 km/s) and a slow (~ 0.4 km/s) ion populations.

18 BEAM DELAY DEPENDS ON DEAD TIME, I.E., PERSISTENCE

19 WHY DOES THE DL FORM? + a fifth species, electrons reflected from the boundaries on the upstream end walls. This balances the current through the DL.

20 LIEBERMAN AND CHARLES MODEL Because the upstream radius is smaller than the downstream radius, an additional source of upstream ionization is required at low pressures, which is supplied by the accelerated group of electrons 1 8eTe V T nupstream ( ne nebeame ) e 4v m thi V T DL e floating wall e And upstream density decreases if DL vanishes

21 RF THRESHOLD FOR DL FORMATION SERENDIPITOUSLY DISCOVERED beam appears for f > 11.5 MHz LIF measurements of the downstream IVDF versus antenna frequency obtained 124 cm downstream of the rf antenna The reference iodine spectrum is also shown.

22 STRAGGLING IONS APPEAR UPSTREAM FOR F < 11.5 MHZ ion acceleration into sheath incomplete for f < 11.5 MHz LIF measurements of the upstream IVDF versus antenna frequency obtained 95 cm downstream of the rf antenna (on upstream side of DL). The reference iodine spectrum is also shown. Note, antenna frequency axis reversed.

23 COINCIDENT WITH DL APPEARANCE, UPSTREAM DENSITY INCREASES DISCONTINUOUSLY beam appears for f > 11.5 MHz Upstream (squares) and downstream (circles) density versus rf frequency. The error bars are smaller than the size of the data points.

24 COINCIDENT WITH DL APPEARANCE, INTENSE ELECTROSTATIC NOISE VANISHES Upstream (squares) and downstream (circles) noise-to-signal ratio versus antenna frequency

25 ELECTROSTATIC NOISE AND BEAM APPEARANCE EVIDENT IN DOWNSTREAM RETARDING FIELD ENERGY ANALYZER MEASUREMENTS AS WELL electrostatic noise appears beam appears for f > 11.5 MHz

26 ELECTROSTATIC NOISE CONSISTS OF WELL-DEFINED HARMONICS OF AN ION-ACOUSTIC-LIKE WAVE C s = 6.4 km/sec. For the 17.5 khz wave V phase = 7 ± 1 km/sec

27 ION FLOW MEASUREMENTS CONSISTENT WITH BEAM DRIVEN INSTABILITY THAT SUPPRESSES DL FORMATION Beam current too large, upstream ion acceleration in pre-sheath decreases, beam vanishes, noise appears, and upstream density drops C s Upstream (squares) and downstream (circles) ion beam velocity versus antenna frequency. DL gets stronger and stronger as frequency decreases (beam energy increases) and then DL abruptly collapses.

28 COMBINED PULSED AND ANTENNA FREQUENCY STUDIES TO EXPLORE BEAM FORMATION PHASE Background Beam Moderate mirror ratio of 30 case persistent ion beam Wave amplitude

29 CLEAR CORRELATION WITH FASTER & MORE INTENSE BEAM AND APPEARANCE OF INSTABILITY ~7.2km/s 8 km/s Faster, Mirror Large mirror ratio more of ratio, intense 30, no large waves beam waves before waves appear

30 LARGE MIRROR RATIO CASE SMALL MIRROR RATIO CASE beam-wave anti -correlation

31 HIGHLIGHTS Double layers form spontaneously in expanding, low pressure, high density plasmas Double layers require some tens of milliseconds to form in a pulsed discharge unless plasma from previous pulse persists The theoretical prediction of increased upstream ionization due to double layers has been verified in an expanding helicon plasma Stronger double layers with larger beam/background density ratios result in excitation of beam-driven ion acoustic instability which suppresses double layer formation ( threshold ~ 1/Vw p ) Ions in the pre-sheath of the double layers accelerate to a common, bulk, sound speed and pressure threshold difference for beams in argon and xenon plasmas reproduced in PIC model

32 THE PRE-SHEATH AND SHEATH REGIONS OF THESE DLS ARE ACCESSIBLE WHAT HAPPENS IN A MULTI-ION SHEATH QUESTION? For a single ion sheath, energy and particle conservation (cold ions) : n n x o u i o 2 e( x) 1 2 Mu Assuming Boltzmann electrons: Solution of Poisson s equation, demands Bohm sheath criterion ( ), is ion speed at sheath edge ( e kt ) e n ( x) n e e o 2 d e( n n ), u > kt M (sound speed) o 2 e i o e dx But Reimann s generalized Bohm criterion for multi-ion pre-sheaths has two interesting solutions for low temperature plasmas: o Case 1: Each species is lost to the sheath at its own Bohm velocity V s T Case 2: All species lost to the sheath at a common velocity e j 2 C s V C s sj m is j n n e0

33 Background XE BEAM AT VERY LOW PRESSURE, BUT NO XE BEAM AT HIGHER PRESSURES FOR WHICH AR BEAM STILL OBSERVED When the ad hoc expansion parameter in the PIC code is set very high, there are beams for high pressure Xe as well as low pressure Xe and Ar. Contrary to experimental results. By reducing the expansion parameter, we achieve a situation more like what is observed experimentally. Unimodal Distribution Beam In the high pressure Xe case the beam and the background coalesce into a more or less unimodal structure. Beam

34 SCALING OF THE PIC CODE XE VELOCITY IN MIXED AR-XE PLASMAS AS FUNCTION OF AR FRACTION CONSISTENT WITH MEASUREMENTS Experimental Data I. Bilou, Ph.D. Dissertation, WVU (2009) Qualitative agreement between the experimentally measured scaling of the Xe velocity with argon fraction and the PIC code.