Cosmic-Ray Generation by Pulsars

Relativistic nonlinear plasma waves in a magnetic field

“…Kennel et al (1973) found exactly the same thing for transverse electromagnetic waves. In their solution, the effective equality of ion and electron masses eliminated the electric field E x parallel to the direction of wave propa gation, which has complicated attempts at solution since the original work of Akhiezer and Polovin (1956).…”

“…In the limit K '2 -.0 (7.7) corresponds exactly to the dispersion relation obtained by Kennel et al (1973). This wave is not a sine wave but a "sawtooth"; dEy/d is virtually constant between = 0 and rj = n and then abruptly changes sign.…”

“…We shall not write the results here, but simply state that as Kennel et al (1973) noticed, the electromagnetic and particle energy fluxes are equipartitioned in the limit q.>>1.…”

“…In addition, following Kennel et al (1973), we change variables from (x, t) to phase n1= w(t-A-), where w is the frequency and B the normalized phase velocity.…”

“…Kennel, Schmidt and Wilcox (1973) found that when ions as well as electrons are driven relativistic by a plane wave propagating in an unmagnetized plasma, there is an upper limit to the cosmic ray number flux which can be transported by a wave of a given, amplitude, above which the wave encounters a cutoff. The plasma wave cutoff flux corresponds to the lower limit on density for which the hydromagnetic approximation is valid.…”