Simulation of Multi-Steady States in Low Temperature Gas Discharge

Plasma Science Technology, Vol 6, No 5, Oct. 2004Simulation of Multi-Steady States in Low TemperatureGas DischLi Hong(李弘)2, Hu xiwei(胡希伟)University of Science Technology of China, Hefei 230026, China2 Huazhong University of Science Technology, Wuhan 430074, ChinaAbstract This article presents hydrodynamics simulation of multi-steady states and modetransition by DC-bearm-injected gas discharge, and provides a model approach to hysteresis anddistinct forms of multi-steady states. The critical transition conditions of the three discharge modes(temperature limited mode, Langmuir mode, and space charge limited mode)are estimated to beependent on the gas pressure and the filament temperature. Various forms of the multi-steadstates in gas discharge can be uniformly explained by the displacement of the mutant positionsThe simulation results are in a good agreement with those of the experimentsKeywords: multi-steady states, gas discharge, simulationPACs:52.801 Introductioncathode sheath. In SClM. the virtual cathode sur-rounding the cathode filaments reflects the majorityChaotic behaviour, including multi- steady statesof beam electrons, and leads to a discharge currentself-oscillations and various routes to chaos in themuch lower than that in TLM. Langmuir mode dis-thermionic discharge at a low pressure, has beerplays similar traits as temperature limited mode, ex-studied for years both experimentally and theo- cept that the cathode in LM acts as a double-sheathetically [1,2,3. The hysteresis that one observes in by which the discharge current is weakened,whilethe discharge current-voltage characteristic curve, as in tLM the cathode in this article acts as a sin-well as the self-oscillations of the discharge current, gle sheath. Different from beam electrons ejectedhave been treated by non-linear dynamic and chaosfrom the filaments under the conditions of highertheory 4, 5, 6. In the typical discharge parameters temperature and lower directional velocity, thermalthere exist multi-steady states(hysteresis)between electrons come from ionized argon atoms and part ofmode transitions between steady modes. The lower am electrons, from which most of their energy wasthe discharge current I and voltage Vd, and mutantranch of the I-Vd curve is widely known as a space tion from the Maxwellian distribution, we divide thecharge limited mode(SCLM), and the upper branch electrons into beam ones and thermal ones.Henceis the temperature limited mode(TLM), while the we can construct a hydrodynamic model with triplemiddle one, the Langmuir mode(LM)only appears components: beam electrons, thermal electrons andconditionally. In this paper, simulation hydrodions, which are represented by subscript b, t and inamic models based on a magnetic multi-pole devicewith hot cathode filaments are built up to describestability criterion of cathode sheath and multi-steadyWhat attracts our attention is that the filament ra-states in gas dischargedius(0.1 mm)is much smaller than the Debye length(1 mm). In respect of cathode sheath region, we2 Cathode sheath in gasprefer the cylindrical pattern to the plane patternBy assuming that the length of cathode sheath isdischargemuch shorter than the collision mean free path andGas discharge with emissive hot filaments中国煤化工 visionless.0wectron andcrates different discharge modes by distinguishing ruledCNMH G the flux corPlasma Science Technology, Vol6, No 5, Oct. 2004Eg=0(Vicm16886cm)V=24v一E=45029cmV=26VN/107Fig.2 The electric field versus ion density in the singleFig. 1 The sheath voltage versus ion density in the dousheath of lmble sheath of TLMOut of the virtual cathodeservation principle(r)where u(r)Tf 2丌memeV(r)-vvelTi means the ion current and Vo means theWith Poisson equation we obtain the numericalsimulation results of the double sheath and thesuming thermal electrons follow the Boltzmanngle sheath, as shown in Figs. 1 and 2, respectively,distribution we havedescribing the relationship of the sheath voltage andhe electric field on the filament surface with the iondensity on the boundary of the plasma regionWhen there are beam electrons ejected from thewhere T means the thermal electron temperaturecathode filaments, Langmuir criterion is employed toand ntu, the thermal electron density on the bounddefine the ratio of ion current to beam electron 7)ary of plasma areaAn improved Langmuir criterion on the cylindricalProvided that only part of the beam electrons withpattern given below leads to a necessarily lower iona velocity above the critical valuecurrentuve= v-(2eVve)/mes1+B2+Bcan pass through the virtual cathode(Vve ),andrest are thrown back to the filaments again. Therefore. the beam electron density on both sides of theThe factor g concerned with the shape of cathode,virtual cat hode can be obtainedand the dimensionless factor B are described respecIn the virt ual cathodeb()=rkTexpdu+Distinct from TlM, the existence of the virtualthode in lm, on which the electric fieldkTr. du,(4) zero, leads to the simplification of the left side ofquation(6). In conclusion, the threshold value ofthe ion current density(as well as the ion density)where uxe=√(2e·V(r)-w}/m中国煤化工 an that o2490CNMHGLi Hong et al.: Simulation of Multi-Steady States in Low Temperature Gas Dischargev201.0Fig 3 Four mutant thresholds versus gas pressure心支为18Fig5 Multi-steady states in gas dischargeTaking the four mutant thresholds as a whole, weFig 4 Four mutant thresholds versus filament temper- find out that the displacement of the four mutantfundamental to thestates, hence bringing about different discharge phe-3 Mutant thresholds of modenomena such as hysteresis, tri-stable and double-transitiondouble-stable(shown in Fig. 5). The statement pro-vides a reasonable and uniform explanation on themulti-steady states phenomena andConcerning the equilibrium equation of ion gen- agreement with the experimentseration and depletion, four mutant thresholdsderived from the stability analysis of the cathodesheath equations. Figs. 3 and 4 illustrate their de-pendence on the gas pressure and the filament tem-Referencesperature, respectively.It should be pinpointed that in Fig. 4 V'cI(1 Ping Y, YuC x, Xie J L, et al. Physics of Plas-LM upwards mutant voltage) and Vc2(the criticamas,2001,8(11):5006~5012voltage of the discharge extinguishment) increase ac2 Lee Hae June, Lee Jae Koo. Physics of Plasmas.dingly as the filament temperature T rises, while1998,5(8):2878V2 (the Lm downwards mutant voltage)and Vc3 Greiner F, Klinger T, Klostermann H, et al. Phys.the critical voltage of the discharge breakdown)keepRev.Let.,1993,70:3071Unchanged. Because a higher filament temperature4 Arnas Capeau C, Prasad G, Bachet G, et alwill generate more beam electrons, the correspondPhysics of Plasmas, 1996, 3(9):3331ing critical condition of cathode sheath requires a5 Knorr G, Plasma Physics and Controlled Fussionlarger inflow of ion current, which may explain the1984,26:9494 Uniform explanation of7 Langmuir I. Phys. Rev., 1923, 21: 419multi-steady statesE中国煤化工 aust.edu. cnCNMHG2491