Review of the gyrotron theory

This review is focused on present studies of beam-wave interaction in high performed during last 15 years by the co-authors. All results are gathered in can tentatively be entitled: “Megawatts rahertz and beyond” and “Miscellane were performed using either non consistent code MAGY [1], or self stationary, multimode code based on lated in Ref. [2], or using quasi-linear a the dependence of the electron current tensity of the RF field is described (see, e.g., [3]).

The second issue requiring a carefu the start-up scenario, i.e. analysis of m excitation of the desired mode followe mode into the region of the most efficie rule, it requires passing through the re excitation into the region of hard sel scenario in long-pulse and CW regime by varying the external magnetic field mod-anode voltages and the beam curre cept was formulated in Ref. [5]; the re dies was given in Ref. [6].)An exa through these regions is shown in Fig. 2 Review of the gyrotron theory Fast voltage rise.Typica much shorter than the voltage always assumed that the amp follows a slow voltage rise [5, this case the voltage rise in guns will cause, first, oscillati with a lower frequency that c nostic channels used in plasm gyrotrons deliver the power.A tion of such parasitic modes voltage rise is fast enough (Fig. Terahertz and beyond.In this section we discuss, first, the role of such factors in electron beams that become more pronounced with the wavelength shortening, viz., the azimuthal nonuniformity of electron emission and the finite thickness of electron beams.The section also includes consideration of some possibilities of operating at high cyclotron harmonics allowing to increase the wave frequency at given magnetic fields. Azimuthal nonuniformity.The azimuthal nonuniformity of electron emission reduces the efficiency of gyrotrons and also affects the mode interaction.As known (see, e.g.[3] and references therein) the interaction between two modes is purely amplitude when their frequency separation exceeds the width of their resonance curves z ); similar conditions can also be written for three-wave interaction.
In the case of azimuthally nonuniform emission the electron current density can be represented as superposition of azimuthal harmonics; thus, certain harmonics can play a role in changing the nature of interaction between the modes.These issues were analyzed in Refs.[10,11].
Beam thickness.The classical theory of gyrotrons is based on the assumption that an electron beam has no spread in radii of electron guiding centers (a thin annular electron beam).The finite spread causes efficiency degradation and may also affect the mode interaction in soft and hard excitation regimes [12].For a 670 GHz gyrotron developed jointly by IREAP and IAP these effects were studied in Ref. [13].
A certain contradiction between requirements to the electron spread in guiding center radii and in velocities should be mentioned.For reducing the velocity spread it is beneficial to form quasi-laminar electron beams.However, the radial spread in such beams is relatively large.The trade-off between these requirements, which allows one to optimize the device efficiency, was studied in Ref. [14].
Operation at cyclotron harmonics.Gyrotron operation at cyclotron harmonics has a long history.In recent years, some issues important for operation at cyclotron harmonics were studied in [15][16][17][18].
Miscellaneous.This part of the presentation will be devoted to consideration of such effects as after-cavity interaction, efficiency and start currents in gyrotrons with tapered resonators, formation of the axial field structure in open resonators, effect of reflections, mode switching [19] and dynamics and stochasticity in gyrotrons with overlapping of cyclotron resonances [20].

Fig. 1 .
Fig. 1.Excitation of a pair of distant sid excitation of a pair of close sidebands in a operating in the TE 31,20 -mode

Gregory S. Nusinovich d
Applied Physics, University of Maryland, College Park, M goryn@umd.eduting results of the h-power gyrotrons presenter and his three groups that s and above", "Teeous".All studies n-stationary, self- f-consistent, non- equations formuapproach, in which density on the in- d by polynomials ion the attention is ction in MW-class modes.Results of Fig. 1 demonstrate with a certain frene.Since the most ime of hard selfe parasitic modes region of soft self- ll.ebands followed by a 170 GHz gyrotron ul consideration is methods of initial ed by driving this ent operation.As a egion of soft selflf-excitation.Such es can be realized d, the cathode and ent.(Original con- eview of later stuample of passing 2.

Fig. 2 .Fig. 3 .
Fig. 2. Horizontal axis shows the t proportional to the beam voltage orbital electron velocity squared (t the mod-anode voltage).The zone ating mode (dashed) is surrounded frequency (lower voltages) and low parasitic modes.Gyrotron trace I d ponds to the diode-type electron gu when during the voltage rise the and mod-anode voltages remains c