Question

4.42. Ion waves are generated in a gas-discharge plasma in a mixture of helium gases. The plasma has the following constituents: (a) Electrons of density no and temperature KTe (b) Argon ions of density nA, mass Ma, charge + Ze, and temperatureC: and (c) He ions of density ng, mass MH, charge+e, and temperature 0 Derive an expression for the phase velocity of the waves using a linearized one-dimensional theory with the plasma approximation and the Boltzmann relation for electrons

Answer 1

Form Boitzman relation n = n_0 e phi_1/k The plasma approximation gives Zn_A1 + n_H1 = n (after considering) The equation of continuity gives iwn_A1 = n_A ikv_A1 iwn_H1 = n_H ikv_H1 and the equation of mohon gives M_A(-iw)v_A1 = M_A partial differential v_A1/ partial differential = Z E_1= Z (-ik phi_1) M_H (- iw) v= M_H partial differential v /partial differential = eE_1 = e (-ik phi_1) from these M_A (iw)x_A1 = z (-ik phi_1) M_H (-iw) v_H1 = (-ik phi_1) M_A (-iw) v_A1/Z = e(-ik phi_1) M_H(-iw) v_H1 = e (-ik phi_1) Comparing & M_A(-iw) c_A1 = Z M_H (-iw) V_H1 we get w^2 /K^2 = K /n_0 [Z^2na/M_A + n_H/M_H] phase velocity is v_ phi = w/k = squareroot KT_c/n_0(Z^2n_A/M_A + n_H/M_H)