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Small Amplitude Wavs
Wave Propagation at an Angle to the External Magnetic
The Energy Exchange Between the Electrons and
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angle approximately arbitrary amplitude assume Cauchy principal value circularly polarized wave component consider constants cos0 cosks cuz+ cyclotron resonance frame cylindrical coordinate cylindrical coordinate system delta function denote derivatives Dirac delta function dispersion relation drift velocity electric field electrostatic wave ellipse elliptic integrals energy density equations of motion exact self-consistent expansion external magnetic field F(cu helical integral in 4.20 intersection ions Kampen kinetic energy kz+0 lab frame Landau last integral linear theory magnetic field Maxwell equations nonlinear nonrelativistic observe obtain order distribution function parabola particle trajectories phase plane phase space Phys plane real roots Resonant Particle sin0 sinkz substitution Taylor series tends to zero tion transformation transverse trapped electrons trapped particles untrapped Vlasov equation wave amplitude wave frame wave of arbitrary waves propagating whistler write yield zero order velocity zero-order