An asymmetric plasma divided by a magnetic filter is numerically simulated by the one-dimensional particle-in-cell code VSIM1D ͓Koga et al., J. Phys. Soc. Jpn. 68, 1578 ͑1999͔͒. Depending on the asymmetry, the system behavior is static or dynamic. In the static state, the potentials of the main plasma and the subplasma are given by the sheath potentials, M ϳ3T Me /e and S ϳ3T Se /e, respectively, with e being an electron charge and T Me and T Se being electron temperatures (T Me ϾT Se ). In the dynamic state, while M ϳ3T Me /e, S oscillates periodically between S,min ϳ3T Se /e and S,max ϳ3T Me /e. The ions accelerated by the time varying potential gap get into the subplasma and excite the laminar shock waves. The period of the limit cycle is determined by the transit time of the shock wave structure.
By the one-dimensional electrostatic particle simulation, the ion beam instability is observed in the plasma divided by the magnetic filter (MF). The strength of the MF is selected to influence only electron dynamics; ions move freely across the MF. There are grounded walls at the left and right ends of the system. Particles hitting the walls are absorbed there. The high temperature and high density plasma (main plasma) faces the low temperature and low density plasma (subplasma) across the MF located at the center of the system. The averaged space potential of the main plasma is higher than that of the subplasma. Due to the potential gap at the MF, ions in the main plasma are accelerated into the subplasma. Depending on the extent of the asymmetry of the system, steady or the periodic (dynamic) state manifests. For the periodic state, high density clumps get into the subplasma and excite the strong ion beam instability. The new clump comes into the subplasma when the old clump reaches the wall.
A ~Iagnetic: filter (~IF) is a localized magnetic field usuall~· generated by an array of permanent magnets. The ~IF installed in the vacuum chamber can separate a plasma into t.\vo regions with different. parameters. The transport of charged particles across the ~IF can be controlled by the properly selected strength of the ~IF due to the difference of the mass. the charge. and the energy. In this paper, the strength of the ~IF is chosen to reflect onlv electrons from both sides of the ~IF: it has little influence on ion dynamics because of large inertia. Due to thermal insulation of electrons by the ~IF. a subplasma with low density and low temperature can exist adjacent to a main ph1sma with high density and high temperature.The asvmmetric plasma divided by the ~IF is numericallv sin;ulated. The one-dimensional particle-in-cell cod~ VSI1IlD 1 l is used. Full d~'namics of electrons ancl ions are followed under the electrostatic approximation. ~lass ratio is mi)nle = 1836.The basic ph:yrsics observed in this system are reported in references 2 and 3. Reference 4 has added detailed measurements to clarifv the mechanism under-1\'inrr the j)hvsics. \Ve selected. N -1 , which is propor-tional to the plasma production rate in the subplasma. as the parameter to control the asymmetry of the system. Depending on the asymmetry, the system exhibits a static state or a dynamic state. \Ve have observed Hopf bifurcation at the critical point between the static regime and the d~·namic reginw: the stntionar~· solution changes from the sta.ble fixed point to the stable periodic attractor (limit cycle) as Ni~ 1 reduces. The transition between two bifurcated states is discontinuous at the boundary.In the dynamic state, the electrostatic potential in .the subplasma ¢s shows the self-sustained oscillation. 208The minimum and the maximum of ¢s are rv 3Tse and rv 3TMe (Tse < TliJe). respective!~·. The potential in the main plasma ¢ lii is almost constant ( rv 31~[ e) with small ripples synchronized \\'ith the autonomous oscillation in the subplasma. The modulnted ion beam accelerated by the potential gap 1Jllf-¢s around the ~IF excites the shock wa~;e in the su bplasma. The shock wave structure has faster nnd slower shock fronts. The approaching faster shock front to the grounded wall has the effect to decrease 0 8 because the electrons in front of the faster shock front is pushed into the electron-free ion sheath next to the wall. \\Then tlw slower shock front is absorbed b\· the wall. c/Js starts increasing due to the difference between the smaller ion flux going into the \vall and the larger ion flux coming into the subplasma across the ~IF.The reason whv the bifurcation is discontinuous at the critical point i~ explained as follows. \iVe can assume that in the dynamic regime the initial state is the unstable fixed point and the solution of the system mmTes to the stable attractor. The picture is illustr<1ted as follows. Due to the thermal noise. the potential gap is modulated slightly. The \veak shock wave produced b~· the veloc...
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