The concept of charge is developed relativistically by assuming that there is a linear relation between point charge (e) and point mass (m) of the type: [Formula: see text] where ζ is a scalar parameter which is unchanged in all reference frames. The theory shows that charge, in a relativistic development based on this hypothesis, depends in general on the velocity of the particle carrying the charge, and the latter vanishes at the speed of light. The hypothesis (1) also implies that charge depends on the scalar and vector potentials of the electromagnetic field. These conclusions are in qualitative agreement with experimental observation.
An analysis of the azimuthally symmetrical, high-frequency eigenmodes of a cylindrical metallic waveguide partially filled with a magnetized plasma is presented. Equations that permit calculation of the dispersion curves for four families of electromagnetic and electrostatic modes are derived. Numerical solutions are presented to facilitate the development of devices for generation of high-power electromagnetic radiation, charged particle acceleration, and other applications of plasma waveguides. The dependence of the cutoff frequencies, and dispersion curves of various modes on the ratio of the plasma radius a to the waveguide radius R is studied in detail. Space-charge modes are found to be strongly dependent on the radius ratio a/R. The coupling of the dispersion curves of different modes and the variation of the cutoff frequencies of HE waveguide and cyclotron modes with cyclotron frequency are illustrated for the partially filled waveguide.
A theory of a planar wiggler free-electron laser with ion-channel guiding is developed. An analysis of the quasi-steady-state electron trajectories is first obtained by solving the equations of motion for an electron in the ion-channel electrostatic field and the wiggler magnetostatic field. Next a sixth-degree polynomial dispersion equation for electromagnetic and space-charge waves in the wiggler is derived. Numerical solutions of the polynomial equation yield the complex wave number as a function of the frequency of the waves. These results are used to illustrate the dependence of growth rate–frequency curves on the ion-channel frequency, and the peak growth rate and corresponding wave frequency as functions of the ion-channel frequency.
The self-electric and self-magnetic fields of a relativistic electron beam passing through a helical wiggler and ion channel are analyzed. A numerical study shows that for a low energy, high density beam the self-fields can produce very large effects.
A linear thcor) is dcielopcd for drift iiitvcs Bith frequencies betiiecn the electron and ion bouncc frequencics in a collisionless plasma confined to a magnetic quadrupole. A n integro-direreniial cifcntaluc equation U hich allot+s for large ion-Larmor-radius cffccts. temperature gradients. and radial \nri;ition of the eigenrunction is dcriied from the linearized Viasot equation. The fundamental drift mode obscrtcd in the L'MIST stcadj-state quadrupole has one full ttaielength around a closed magnctic field line nith the electrostatic w a t e potential antisJmmciric about the maximum field points. BJ numsrical mitition or the cigcnialue equation. the theoretical dispersion curie for this mode IS extended t o short t i a i c l e n g t h ~ and the \ariation of the corrtsponding potential along a field line 1s determined. I . I S T R O D L ' C T I O SESPERISlEsTAL studies of electrostatic wives in a plasma confined to a magnetic quadrupole are current13 being carried out at the Lnii,ersity of Jlanchester Institute of Science and Technology (UMIST). Drift ivaves x i t h one full u.a\elength around a closed magnetic field line ha\,e been observed to occur spontaneously. C.ARTER et d. (1951 ) ha1.e made a theoretical and experimental study of these drift Lvaves in the UMIST quadrupole. Their theoretical and experimental dispersion curves are in good agreement throughout the entire axial \vave number range from k, 2 0 . 6 cmi to k , 2 1.6 cm-'. The general shape of the theoretical curws shoiving ~a v e amplitude variation along a field iine is also ~vc.11 reproduced b! the experimental results in this k , range. This mode is belicxd to be excited b! . a dissipati\,e trappcdclcctron mechanism \vhich \vas in\,cstigated recently by NI'ILLETT. i ~i tri. ( 19S6)..Although the obsei\'ed spectrum of spontaneous drift \\'a\ es in the ChI!ST
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