In some works it was shown that under the action of stochastic field the charged particle, in average, gradually obtains energy. But stochasticity is only mean of brief description of system, and it cannot be reason of real phenomena. Analysis of relationships obtained in relevant works shows that particle energy increase takes place due to presence of power at resonant frequencies: in static magnetic field it is cyclotron frequency, in isotropic plasma it is plasma frequency, for free particle it is zero frequency (that is, particle energy increases due to one way acceleration). In absence of constant magnetic field, in periodic electric field, there are two possible variants of particle motion, depending on the value of integral of electric field strength by period: pure periodic motion (if the integral is equal to zero) and sum of periodic motion and constant acceleration (if the integral differs of zero). In the second case the particle energy increase approaches the square of time. If particle moves in the field changed stochastically then the velocity obtained by particle during time , increases with increase, in average, as , the energy, in average, increases proportionally to , and the field projection on the fixed direction averaged by time decreases, in average, as . The last gives some grounds to say about the possibility of particle energy increase in absence of constant field component, though, really, particle velocity change during some time interval is possible only for nonzero value of field averaged over this time interval.
If electric field strength changes periodically in time then its Fourier transform is linear combination of delta-functions. If the frequency resonant for the given system makes vanished the argument of one of the delta-functions then particle energy grows with time, in average, as square of time. In the opposite case a periodical motion takes place. But for the spectrum of stationary stochastic signal the limited and nonzero may by the relation of square (not the first power, as for the periodic signal) of Fourier integral of the function extended with zero out of the time interval with duration to value. The limit, at , of the averaged by realization absolute value of the mentioned relation characterizes power spectral density, which is connected with Fourier transform of correlation function. And if this Fourier transform is limited and nonzero for any resonant frequency then particle energy in such field grows with time, in average, linearly. And appearance of effect of charged particle energy increase in stochastic field in relevant works was connected with option of such dependence of correlation coefficient on time that its Fourier transform is limited and nonzero at all frequencies.
If electron moves under action of sinusoidal field and undergoes to collisions with neutrals then field projection on the direction of its movement is described by sinusoid with jumps of phase. In the collisionless electron motion under the action of the same sinusoid with jumps of phase the absolute value of electron velocity is changed with the same time dependence, but the spatial motion of electron may differ considerably and it, usually, covers region with greater dimension. But if one restricts the region for electron motion and imposes the restriction on the absolute value of field strength then maximal electron energy will be the largest in the case of application of the maximal strength by turn in opposite directions. Replacing of such piecewise-constant dependence with sinusoidal one decreases maximal electron energy twice. But introduction of any stochastic jumps, in any case, does not permit to exceed the maximal electron energy attainable in the mentioned piecewise-constant dependence.
As the path length of electron between ionization usually much greater than its free path, the development of ionization process assumes essentially collisional character of electron motion accompanied with collisional heating, which should be accounted in investigations for process of ignition of high frequency low pressure gas discharge in the complicatedly varying field.
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