H. "Naitou

K. Ohi

O." Fukumasa

Y. Tauchi

National Institute for Fusion Science (NIFS-Repository)

§32. Bifurcation in Asymmetric Plasma Divided by a Magnetic Filter Naitou, H., Ohi, K., Tauchi, Y., Fukurnasa, 0. (Yamaguchi Univ. Eng.) 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 numer-icallv 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. Left and right boundaries of t.he system. x = 0 and x = L.r = 400. are grounded \~valls. Particles hitting the walls are absorbed there. The ~IF locates at the center of the system ( .r = .r: 11! F = 200). The direction of the magnetic field is in the z-axis. The spatial profile of the magnetic field strength is given by 2 2 l B(x) = Bo exp [ -0.5(x - XllfF) /aM F , (1) where Bo = 0.5 and aMF = 12. The main plasma with Tlii e = 4 and TJII i = 0.1 exists in x 1\.I F ::::; x ::::; L.r. whereas the subplasma with Tse = 1 and Tsi = 0.1 exists in 0 ::::; x ::::; .T.r..f F· Here. TJ\Ie and Tse are electron temperatures, and T~Ii and Tsi are ion temperatures in the respective plasmas. Hydrogen plasma is assumed. ~lass ratio is mi)nle = 1836. The basic ph:yrsics observed in this system are re-ported 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-. o • 1n tional to the plasma production rate in the subplasma. as the parameter to control the asymmetry of the sys-tem. 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 peri-odic attractor (limit cycle) as Ni~ 1 reduces. The tran-sition 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. 208 The 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 oscil-lation in the subplasma. The modulnted ion beam ac-celerated 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 un-stable fixed point and the solution of the system mmTes to the stable attractor. The picture is illustr<1ted as fol-lows. Due to the thermal noise. the potential gap is modulated slightly. The \veak shock wave produced b~· the velocit\· modulated ion beam reaches the left wall. If the redu~:tion of GJs bv the approaching shock wave is bigger than that of the former potential modulation. the stronger shock wave is formed. This positive feed back process continues until the maximum potential of the sub plasma goes up to rv cjJ 1\I. The growth rate of the os-cillating part of C/J s is measured in the dynamic regime. The growth rate decreases down to zero at the critical I)oint as N- 1 increases. In the static regime. there is 1n no positive feedback because bulk electrons mitigate the effect of the approaching shock \vave. So the threshold exists for the positive feed back to occur. \vhich may be the ratio of the ion beam flux from the main plasma to the plasma density in the subplasma. In reference 4. the control parameter is fixed during the temporal e\Tolution of the simulation s:vstem. It is natural to expect that the system treated here exhibits the hvsteresis if the control parameter is changed very slowl;r. The hysteresis in the asymmetric plasma divided by the ~IF is studied in reference 5. Reference 1) Koga, K .. Naitou, H .. Kawai. Y .. J. Phvs. Soc. Japan 68 (1999) 1578. 2) Naitou. H .. Ohi. K .. Fukumasa. 0 .. Rev. Sci. Instrum. 71 (2000) 875. 3) Ohi. K .. Naitou. H .. Tauchi. Y. Fukumasa. 0 .. Phv. of Plasmas 8 (2001) 23. 4) Oh(, K., Naitou, H., Tauchi. Y., Fukumasa. Plasma Plws. Control. Fusion (submitted). 5) Ohi, K., Naltou, H., Tauchi, Y., Fukumasa, 0., Itoh, K., J. Plasma Fusion Res. SERIES (submitted). 

Bifurcation in Asymmetric Plasma Divided by a Magnetic Filter

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