ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The physics of ultrahigh density compressional oscillations of a non-neutral plasma has already been discussed. Here, one technical facet will be analytically plumbed; namely the frequency of such oscillations. These oscillations are governed by differential equations whose solutions involve elliptic integrals of the third kind. Nevertheless, without studying the properties of these integrals, a procedure is demonstrated which permits the development of an analytic formula for the frequency of these anharmonic oscillations. This frequency is shown to be proportional to the cyclotron frequency ωc with a constant of proportionality that depends on the ratio of the difference between the radii of the outer and inner turning points divided by the sum of the radii of the two turning points. These radii, in turn, depend on two constants of integration that represent the energy of the compressional oscillations and the amount of charge in the plasma cloud. The final result of the analysis is that the frequency varies only from ωc/(square root of)2 when the above ratio is small to (2/3)1/2ωc when the ratio is large. These limits are also obtained intuitively.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530557
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