Scenario for the establishment of an electron beam ''squeezed state'' in a magnetically insulated vircator. A. E. Dubinov. Russian Federal Nuclear Center ...
Scenario for the establishment of an electron beam ‘‘squeezed state’’ in a magnetically insulated vircator A. E. Dubinov Russian Federal Nuclear Center — All-Russian Scientific Research Institute of Experimental Physics, Sarov (Arzamas-16)
~Submitted July 29, 1996! Pis’ma Zh. Tekh. Fiz. 23, 29–33 ~November 26, 1997!
A 2.5-dimensional particle-in-cell code was used to simulate different scenarios for the establishment of an electron beam ‘‘squeezed state’’ in a magnetically insulated vircator. Vircators with and without anode foils were compared. It was found that the squeezed state is established in both cases but the dynamics of establishment differ. © 1997 American Institute of Physics. @S1063-7850~97!02311-2#
Generators of microwave radiation with a virtual cathode ~vircators! are attracting increasing attention among researchers.1,2 Among these devices, particular mention should be made of vircators with magnetically insulated diodes in which a virtual cathode is formed in a drift tube of diameter much greater than the anode diameter.3 Usually these systems do not have a transverse anode foil so that they can be called foilless vircators. The dynamics of the formation of a virtual cathode in a foilless magnetically insulated vircator was simulated in Ref. 4. It was shown that a so-called ‘‘squeezed state,’’ characterized by a low velocity and high electron density, is established in the beam, and the front of this squeezed state moves together with the virtual cathode in the direction opposite to injection and stops near the cathode in the anode tube. In order to explain this phenomenon, the authors of Ref. 4 analyzed a model based on the balance of the pressure forces in the cross sections on different sides of the step — a transient anode tube in the drift tube. However, this model disregards the conditions at the step itself, where a thin electron-transparent foil or, say, a thin plasma layer, may or may not exist. It is natural to expect that different conditions at the step may lead to different scenarios for the formation of the virtual cathode ~significant differences in the electron dynamics with and without an anode foil have been observed in an ordinary vircator, see Ref. 5!. In this context, our aim here is to continue the study of the squeezed state in a magnetically insulated vircator started
in Ref. 4, and particularly to determine whether the same or different scenario for the establishment of the squeezed state may be achieved under different conditions at the step. For this purpose we used the KARAT computer modeling package6 which uses a 2.5 dimensional particle-in-cell ~PIC! code and was kindly supplied by V. P. Tarakanov. The region modeled and the required dimensions are shown in Fig. 1. It was assumed that a uniform longitudinal magnetic field of 50 kG was applied to the entire system and a 500 kV voltage pulse was applied to the diode gap. Two versions, with and without a foil positioned at the diameter step, were compared. It was found that in both cases, the amplitude of the cathode current was approximately 17 kA and a squeezed state was formed. The evolution of the squeezed state can be conveniently studied using instantaneous phase portraits of the beams in the coordinates ( v z ; z). Phase portraits at various times ~1, 2, and 3 ns! are given in Fig. 2a for a vircator with a foil and in Fig. 2b for a foilless vircator. An analysis reveals that in the vircator with the anode foil, the squeezed-state region of the beam develops more slowly than in the foilless vircator, leaving behind a ‘‘phase bubble’’ in the foil region. The existence of this bubble can be explained by the fact that the potential near the step is forced to remain equal to the anode potential. The nature of the virtual cathode motion and also the motion of the front of the squeezed state were determined.
FIG. 1. Schematic of modeled region ~all dimensions are in millimeter, not to scale!.
870
Tech. Phys. Lett. 23 (11), November 1997
1063-7850/97/110870-02$10.00
© 1997 American Institute of Physics
870
FIG. 2. Instantaneous phase portraits of the beam in the plane ( v z ; z): a — for a vircator with an anode foil, b — for a foilless vircator.
The laws governing their motion for both cases, calculated with a time step of 250 ps, are plotted in Fig. 3. The opposite curvature of these graphs indicates that the pressure forces at the front of the squeezed state differ in the two cases ~if it is meaningful to talk of a force acting on phase formations, such as the virtual cathode and the front of the squeezed state!. To conclude, the squeezed state in a magnetically insulated electron beam is established regardless of the conditions at the step but these conditions strongly influence its establishment scenario. The author would like to thank V. P. Tarakanov for consultations on the use of the KARAT code.
1
FIG. 3. Laws of motion of virtual cathode ~and front of squeezed state!: 1 — for vircator with an anode foil, 2 — for foilless vircator. 871
Tech. Phys. Lett. 23 (11), November 1997
B. V. Alyokhin, A. E. Dubinov, V. D. Selemir et al., IEEE Trans. Plasma Sci. 22, 945 ~1994!. 2 A. E. Dubinov and V. D. Selemir, Zarub. Radioelektron. No. 4, 54 ~1995!. 3 A. G. Zherlitsyn, S. I. Kuznetsov, and G. V. Mel’nikov, Zh. Tekh. Fiz. 56, 1384 ~1986! @Sov. Phys. Tech. Phys. 31, 814 ~1986!#. 4 A. M. Ignatov and V. P. Tarakanov, Phys. Plasmas 1, 741 ~1994!. 5 V. D. Grigor’ev and A. E. Dubinov, Pis’ma Zh. Tekh. Fiz. 22~7!, 70 ~1996! @Tech. Phys. Lett. 22, 299 ~1996!#. 6 V. P. Tarakanov, User’s Manual for Code KARAT, Berkley Research Associates, Springfield, VA ~1992!. Translated by R. M. Durham A. E. Dubinov
871
