Radius of the cylinder: R Ion an electron cyclotron radii: ρ i and ρ e Ion-atom collision

1. INFLUENCE OF RAMSAUER EFFECT ON BOUNDED PLASMAS IN MAGNETIC FIELDSN. Sternberg and C. Sataline, Clark University, Worcester, MA, USAV. Godyak, RF Plasma Consulting, Brookline, MA, USA EPS2008,Crete Abstract. A study of the fluid model for cylindrical weakly ionized quasi-neutral plasmas in an axial magnetic field is presented. The model takes into account ionization, ion and electron inertia, as well as frictional forces for ions and electrons. Two cases for the electron frictional forces are considered: with the Ramsauer effect and without the Ramsauer effect, while the ion frictional force is defined by the charge exchange process. For each case, the behavior of the plasma parameters for arbitrary magnitudes of the magnetic field, gas pressure and plasma size is presented, making the model applicable for a wide range of discharge conditions and gases. A magnetic field parameter is introduced, which specifies a parameter range for the magnetic field, gas pressure and plasma size where the Boltzmann equilibrium with the ambipolar field for the electron distribution is satisfied. A parametric relation for the magnetic field, gas pressure and plasma size is obtained, which separates the region of weak magnetic field effects from the region of strong magnetic field effects. In addition, analytical transformations between the corresponding parameters with and without the Ramsauer effect are obtained. Notation Relationship between the plasma characteristics with (index 1 ) and without (index 0) the Ramsaeur effect: ●for the magnetic parameters: G1=G0β1/β0 ; β1=0.3β0 αi1/2 if αi ≠0 andβ1=β0/3 if αi=0 ● for strongly magnetized plasma: yb1=yb0β0/β1 ; S1=S0β0/β1 ● in the whole range of β: yb1=yb0(1+G0+G02)1/2(1+G1+G12)-1/2 and S1=S0(1+G0+G02)1/2(1+G1+G12)-1/2 Radius of the cylinder: R Ion an electron cyclotron radii: ρiand ρe Ion-atom collision parameter: αi=R/λi Electron-atom collision parameter: αe=(M/m)1/2R/λe Magnetic parameters: β=(Rλe)/(ρiρe), G=0.64(4+αi)-1/2β Gas pressure: p Ion sound speed: vs With the Ramsauer Effect: αe=50αi1/2 (λi ~p-1/2, λe ~p-1) for αi≠0 αe=30 for αi=0 Without the Ramsauer Effect: αe=15αi (λi ~p-1, λe ~p-1) for αi≠0 αe=10 for αi=0 Discussion of the results Cylindrical plasma in an axial magnetic field Gases with and without the Ramsauer effect : For strongly magnetized plasmasβ>>1: ● the Boltzmann equilibrium relation for electrons is not valid ● the normalized ion density distribution is represented by the Bessel function n/n(0)=J0(2.405(1-1/β)r/R), 0≤r≤R. ● the normalized ion density at the plasma boundary is yb=n(R)/n0 =1.25/β, and the normalized ionization frequency is S=ZR/vs =5.78/β For weakly magnetized plasmas β<<1: ● if the Boltzmann equilibrium relation is valid, then the magnetic field is negligible. The regions of strong and weak magnetic field effects are separated by the parameter value G=1. In the whole range of β ● yb=0.8(4+αi)-1/2(1+G+G2)-1/2 S=2.2(4+αi)-1/2(1+0.59G+0.35G2)-1/2 Continuity equation Fig. 1. Normalized plasma density distribution for αi=1 and varying magnetic field in Argon gas. Increase in gas pressure increases the region where the Ramsauer effect is irrelevant. Fig. 2. Normalized plasma density at the boundary versus the magnetic parameter for Argon gas without the Ramsauer effect. The figure is similar in the case with the Ramsauer effect. Momentum equations for ions Conclusion. We have studied the influence of the Ramsauer effect on the plasma characteristics for a cylindrical plasma with an axial magnetic field. We gave formulas which relate the plasma characteristics for gases with and without the Ramsauer effect. We have found that the Ramauer effect is relevant only for intermediate magnetic fields and that the theory of the cut-off between the regions of weak and strong magnetic fields by the external discharge parameter G is independent of the Ramsauer effect. Momentum equations for electrons References [1] N. Sternberg, V. Godyak and D. Hoffman, Phys.Plasmas 13, 63511 (2006)