NEWSLETTERof the International Consortium“Development of High-Power Terahertz
Science & Technology”
October 2020

№ 16

CONTENT Editorial(Page 1)

How to contribute to the Newsletter Invited papers
 V. Manuilov, A. Tsvetkov, I. Zotova, A.Fedotov, S. Mitsudo, T. Idehara, M. Glyavin, “Optimizationof an electron gun shape for a third harmonic 1.2 THz/CW gyrotron.”(Page2)
 I. Bandurkin, A.Fedotov, M. Glyavin1, T. Idehara, A. Malkin, V. Manuilov, S.Mitsudo, A. Sergeev,
S.Sabchevski, A. Tsvetkov, V. Zaslavsky, I. Zotova, “Design of a third-harmonic 1.2 THz/CW
Gyrotron with an Intentionally Increased Velocity Spread of Electrons.”(Page 10)
 Upcoming events (updated announcements)(Page 23)
 Special journal issues in the field of THz science(Page 24)
 Personalia: Professor A. Litvak at 80(Page 25)
 List of selected recent publications, patents, and new books(Page 27)

EDITORIAL: HOW TO CONTRIBUTE TO THE NEWSLETER
Dear Reader,
We are inviting contributions to the following rubrics:• Research highlights (annotations) presenting the projects pursued by the members of the Consortium.
• Short regular and invited papers.
• Proposals for collaborative research work.
• News from the participating institutions.
• Information about conferences, symposia, workshops, seminars.
• Programs and frameworks for an exchange of visits and mobility of researchers. Job opportunities(especially for young researchers, e.g. postdoctoral positions, specializations, internships).
• Annotations of books, conference proceedings, software and internet resources. Additions to the list of
the recent scientific publications and conference reports at the website of the Consortium(http://fir.ufukui.ac.jp/Website_Consortium/publist.html ).
• Information and announcements about awards and nominations.
• Short presentations of laboratories and research groups belonging to the participating institutions.
Please submit your contributions to the Newsletter as well as requests for information to:Professor Masahiko Tani
Director of FIR UF – Facilitator of
the International Consortium
FIR UFtani@fir.u-fukui.ac.jp

Dr. Svilen Sabchevski
Editor of the website and the Newsletter
Institute of Electronics of the Bulgarian
Academy of Sciencessabch@ie.bas.bg

INVITED PAPERS
Optimization of an electron gun shape for a third harmonic 1.2 THz/CW gyrotron
V.N. Manuilov1,2,3, A.I. Tsvetkov1,3, I.V. Zotova1,3, A.E.Fedotov1,3,S. Mitsudo3, T. Idehara3, M.Yu. Glyavin1,3,*
1Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS),
46 Ulyanov str., Nizhny Novgorod, 603950 Russia
2

3Radiophysical department of Nizhny Novgorod State University,
23 Gagarin av., Nizhny Novgorod, 603950, Russia

Research Center for Development of Far-Infrared Region, University of Fukui (FIR FU),
Bunkyo 3-9-1, Fukui 910-8507, Japan*

Contributed by the corresponding author M. Glyavin: glyavin@ipfran.ru

Abstract. The design of a magnetron-injection gun (MIG) which is appropriate for a CW 3-rd
harmonic gyrotron with a frequency of 1.185 THz and the output power about 100 W, intended for
DNP/NMR spectroscopy applications is described. To improve the mode selection, several
electron-optical schemes are investigated. The MIG allows using both single-beam and double
beam schemes of the gyrotron operation with two different operating modes. Requirements for theelectron beam parameters are formulated. The design of the triode MIG forming two generating
beams with a quality suitable for a third harmonic operation has been accomplished and optimized.
A specific feature of the designed MIG is the possibility to form either two beams or one beamusing the same electrodes configuration and different number of emitting rings. The proposed MIG
design is insensitive to small misalignment and reasonable manufacturing inaccuracy. A key
advantage of the design is that it allows improving the mode selection utilizing an electron beamwith increased velocity spread as proposed in this study. It is shown that it is possible to form two
beams with practically equal and quite high pitch-factors in all range of operating currents andsimultaneously small enough coefficient of reflection from the magnetic mirror despite the large
enough value of the velocity spread.
Key words: gyrotron, terahertz range, cyclotron harmonic, mode selection, helical electron beam, doublebeam magnetron-injection electron gun, numerical simulation.

1. Introduction
The terahertz frequency range (0.1—10 THz) has a number of specific features that make it very attractive
for a wide range of fundamental and applied research in the fields of physics, chemistry, biology and medicine[1–3]. In particular, terahertz waves are promising for diagnostics and spectroscopy of various media, including
electron paramagnetic resonance (EPR) and high-resolution nuclear magnetic resonance (NMR) methods [3].
Unfortunately, the modern sources of coherent THz radiation have serious limits with respect to the output
power.
One of the most promising tubes in the terahertz frequency range are the gyrotrons [4 – 6]. In comparison
with other sources of THz radiation they have relatively small weight, size, and cost and power sufficient for
many of the mentionad applications. Recently the project of a CW gyrotron operating on the third cyclotron
harmonic (15 T magnetic field intensity, 1.2 THz frequency with a power about several Watts) on either TE1 5,6or TE21,4 cavity modes was suggested and optimized [7]. It is based on the utilization of the conventional
single-beam gyrotron scheme. However, the transition towards the THz frequency range sharply increases thedensity of the modes within the cyclotron frequency band.

The excitation of high cyclotron harmonics needs special methods of mode selection for suppression of thefundamental harmonic mode which has a lower starting current. Usually the gyrotrons use electrodynamic(complex cavity) or electronic (multi-beam, axis encircling beam, etc.) methods to improve the mode selection.
For the case of high harmonic number excitation the parasitic modes are far from the cut-off frequency. Itmeans that they are travelling waves and are very sensitive to the velocity spread. To suppress the spurious
travelling modes, the scheme based on the helical electron beam (HEB) with a high (30 — 40%) oscillatory
velocity spread was suggested [8]. It should be noted that an increase in the velocity spread can somewhat
worsen the efficiency of the gyrotron. This, however, is not a critical problem for spectroscopy and diagnostic
application that require small microwave power.
Another way to ensure single-mode operation with high enough microwave power (which needs highelectron beam current) is to use multi-beam schemes [9 – 12]. Recently, in the common proof of principle
experiments of Russian and Japanese teams, the efficiency of this approach for the second cyclotron harmonic
operation with two generating HEBs was confirmed [13]. This made it possible to obtain power of about 10 W
with a frequency of 0.79 THz using a commercially available and relatively inexpensive 15 T superconducting
magnet installed in the experimental setup of FIR FU Center. Thus, to increase the reliability of the singlemode operation with such a high frequency it is better to combine both mentioned above approaches and makethe universal gun design suitable for both the single-beam or double beam operation with high value of thevelocity spread and simultaneously provide a stable electron beam with a high current.
Below the design of the double-beam triode magnetron-injection gun (MIG) forming two generating beams
with the quality suitable for microwave generation with the frequency   3c at the third cyclotron harmonic,
is suggested and optimized. In contrast to the traditional design [14], an operation at relatively low voltage(about 20 kV) imposed by the limitations of the currently available high-voltage power supply is analyzed. The
specific feature of the gun is that it allows forming either two beams or one beam using the same gun geometry.
In the last case, it is provided simply by removing the additional emitter from the cathode surface. The 15 T
cryomagnet with a diameter of a warm bore of 52 mm (made by JASTEC, Inc.) installed in University of Fukui(FIR UF Center) will be used. Realization of the stable single-mode CW generation at the third cyclotron
harmonic will make it possible to create a unique terahertz radiation source for DNP/NMA spectroscopy and anumber of other promising applications.
2. Selection of the injection radii of the electron beams
According to the detailed analysis performed in the previous work [7], the gyrotron can use either TE-15,6 orTE21,4 modes as the operating ones. The coupling factors for such modes are presented in Fig. 1.

Fig. 1. Coupling factors of the electron beam to the eigenmodes of a cylindrical cavity vs. the electron beam injection
radius Rbeam: TE+21,4 (harmonic number s = 3), TE-15,6 (s = 3), TE8,5 (s = 2). The cavity radius Rcavity is equal to 1.488 mm.

Below, the two versions of a gyrotron are preliminary considered: a conventional single-beam gyrotron and adouble-beam gyrotron. In the first case, for the injection radius of 0.85 mm, the coupling factor for both
operating modes is significantly higher than that for the parasitic ones TE±8,5. In the second case, there is also an
external HEB with a radius Rbeam = 1.07 mm. This beam has a fairly strong coupling to the parasitic mode,
however, its use together with the main internal HEB does not violate the selective excitation of the operating
mode (at a reasonable value of the current of this beam) and makes it possible to increase the total current,
allowing increasing the output power of the tube.
3. Evaluation of the admissible spread of the electron beam injection radii.
One of the parameters that must be known before starting the design of the MIG is the spread of the guiding
centers in the HEB. It defines, to some extent, the electron beam current and possibility to manufacture theemitter ring with a good enough accuracy. We estimated the minimum values of the starting currents in Ist min(H) curve, where H is the intensity of the magnetic field for the operating mode TE15,6, and for the mainparasitic mode TE8,5 as a function of the thickness Rbeam of the electron beam. In these calculations, weconsidered the case of asingle HEB with a radius Rbeam = 0.85 mm.
For the simplest model with a fixed longitudinal structure of the microwave field f(z) = sin(πz/L) (where L isthe effective length of the gyrotron cavity), in case when the electron beam has a finite thickness Rbeam, thestarting current can be calculated using a generalization of the well-known formula [5,15]:
 R

R

/2

beam
beam
1
I st  ( ) Gm , p ( R) dR  1 ,Rbeam Rbeam  Rbeam / 22eQL 2  20s  2  s s  d  1  cos ( )   s    s  ,32
mc  0||0  2 s!  d  [1  ( /  ) 2 ]2I st min (Rbeam )  min I st ( H ) ,H

where θ = (ω–sωc)L/v|| is the transit angle, ωc = eH0/mcγ0 is the unperturbed cyclotron frequency,
γ0 = 1 + U0[kV]/511 is the relativistic Lorentz factor, U0 is the accelerating voltage, Q is the quality factor of the
gyrotron cavity, β⊥,|| = v⊥,||/c are the normalized transverse and longitudinal velocities, μ= πgβ⊥0L/λ is thenormalized interaction length, and λ being the radiation wavelength.
The results of the calculation are shown in Fig. 2.

Fig. 2. Minimum value of the starting current Ist min as a function of the thickness of the electron beam for operating mode
TE-15,6 and for the parasitic one TE8,5, expressed in wavelengths /Rbeam.The same value of /Rbeam corresponds to thedifferent values of the magnetic field strength.

With an increase in the HEB thickness, the minimum value of the starting current for the spurious TE8,5
modes dramatically decreases (dashed and dash-dotted lines in the figure), and simultaneously, the starting
current of the operating one TE-15,6 rapidly increases (Fig. 2). Thus, it seems reasonable to choose a beam
thickness of about /5 accepting a compromise: on the one hand, a further decrease in the beam thickness does
not significantly improve the situation; on the other hand, this value seems realistic from the point of view of
the implementation of the electron-optical system.
4. Preliminary adiabatic estimations of the MIG parameters
The gyrotron is based on the same magnetic system as in the project of 0.79 THz double-beam gyrotron at
the second cyclotron harmonic [16]. To ensure high coupling of the two beams with the RF field and goodenough gyrotron efficiency the following HEBs parameters were chosen: Rin = 0.854 mm (0.85 mm),
Rext = 1.065 mm (1.07 mm), gin =gext = 1.3, vin =vext  30 – 40%, Iin , Iext  0.8 A. Here the indexes “in” and“ext” correspond to the internal and external beams, respectively and the values in brackets correspond to theTE21,4 mode. The spreads of the guiding centers Rin, Rext should be less than /5. Here Rin, Rext are partial
beams radii, gin, gext – pitch-factors, Rin, Rext – spread of the guiding centers, Iin, Iext – currents of the beams.
The specified values of injection radii for both operating modes are very close: the difference incorresponding injection radius is less than /50, i.e. 10 times smaller than the admissible value of the guiding
centers spread. This allows to design an universal scheme of the double-beam MIG suitable for utilizing in thesame gyrotron operating at both specified above modes simply by substituting the corresponding cavity inside
the tube (to keep the frequency value of about 1.185 THz for operating mode TE21,4 the cavity radii must be
equal to 1.492 mm).
A relatively low [17] value of an accelerating (cathode) voltage U0 should be preferred in order tosimplify the gyrotron power supply system. On the other hand, to satisfy the cyclotron resonance condition:2  28  3с  3 
 H [T ]

for a fixed maximum value of the magnetic field intensity H which is not higher than 15 T we need to limit thevalue of the accelerating potential to approximately 32 kV. Hence, below we consider a version of the beamshaping system with a total accelerating voltage of 30 kV and maximum beam current of 3 A (total in twoHEBs), which are estimated to guarantee power of about a hundred watts at least. For a more flexible control ofthe parameters of the partial HEBs, we considered a triode scheme of the MIG with an anode voltage Ua ≈ 12
kV.
Preliminary analytical estimation of the electric regime and the MIG dimensions was performed basedon the adiabatic theory of HEB formation system [12]. The laminar electron beam was suggested, so themagnetic-field line to the emitter angle  must be  25. The initial gyrotron parameters, which were further
used for analytical estimations, are summarized in Table1, whereas the preliminary data of MIG estimations arepresented in Table 2.
Table 1.Gyrotron parameters in the interaction space.
Wavelength 
Operating magnetic field Bo
Accelerating voltage UoFirst-anode potential Ua
Beam radii in the cavity Rext (external beam)
and Rin (internal beam) for TE-15,6 mode:and for TE21,4 mode:
Operating beam currents Iext and Iin
Pitch factors g1 and g2
Magnetic-field line toemitter surface angle 0.250 mm
14.9 T
30 kV
12 kV
1.065 mm, 0.854 mm
1.070 mm, 0.850 mm
1.7 A , 1.3 A
1.3, 1.3
 25

Table 2.Basic design parameters of the beam shaping system.
Cathode electric field Ec
Spread of the guiding centers in the cavity,Ro (for both beams)
Emitter width L (for each beam)
Current density jc (for both beams)
Ratio tj of the beam current to the Langmuircurrent (for both beams)
Magnetic field compression
 (external and internal beams)
Emitter inclination  to the axis (external beam)
Cathode radius Rc2 (external beam)
Anode radius Ra2 (external beam)
Emitter inclination  to the axis (internal beam)
Cathode radius Rc1 (internal beam)
Anode radius Rа1 (internal beam)

2.36 kV/mm

/5
1.0 mm
3.0 A/cm2
0.25
71.4, 69.130
9.0 mm
14.6 mm
25
7.1 mm13.5 mm

It is important to note that the chosen emitter width (1 mm for both beams) satisfies the mentioned two
requirements. On the one hand, such width allows to manufacture the emitter ring using the existing technology(manufacturing of smaller ring is much more complicated task). On the other hand, it corresponds to therestriction imposed by the admissible values of the spreads of the guiding centers in the cavity.
5. Results of the electron trajectory analysis of a double-beam MIG
Second step of the MIG optimization is, as usual, the numerical simulation of the beam properties andoptimization of the gun shape.
To simplify the future manufacturing of the electron gun and gyrotron itself and to make it cheaper, thedistance from the gun to the cavity was kept close to the distance (570 mm) in the previous version of the
double-beam gyrotron [16] operated on the second cyclotron harmonic. Besides, the shape of the second anodewas kept the same.
The optimization was done using two-dimensional software EPOS [18]. The final MIG geometry is shown in
Figure 3. The first anode is parallel to the tube axis. The beams parameters calculated according to the model
without the initial velocity distribution (such model usually is used for the first step of the optimization) are
shown in Table 3. Both beams have very close pitch-factors and smooth dependence of their properties on theoperating current.
Table 3. Calculated beams parameters in the nominal regime for an anode voltage Ua = 11.73 kV
jk, A/cm2
1.0
1.5
2.0
3

internal beam
I, Ag
0.44 1.46
0.65 1.40
0.87 1.34
1.31 1.24

v
0.03
0.04
0.05
0.08

jk, A/cm2
1.0
1.5
2.0
3

external beam
I, A
g
0.56
1.44
0.84
1.39
1.12
1.34
1.68
1.24

v
0.04
0.05
0.07
0.10

The calculations show also that the velocity spread  v practically does not depend on any kind of the gungeometry deviation caused by system misalignment or thermal deformation of the electrodes for both theinternal and external electron beams: it varies by no more than (0.3 – 1.0)%, while the pitch factor varies by
no more than 0.12 when the longitudinal shift of the magnetic system in the interval 2 mm occurs. The
sensitivity of the pitch-factor to the radial shift of the first anode is significantly higher, especially for theexternal beam due to the rather small anode-cathode distance and can reach 0.3. The latter effect, however,can easily be counterbalanced by small variations in the anode potential Ua. Due to the cylindrical form of thefirst anode the gun is not sensitive to the longitudinal shift of the first anode.

Fig.3. Shape of the electrodes and trajectories of the electrons in the double-beam MIG at the first anode region. The
anode potential is 11.73 kV.

The key points of the optimized MIG geometry (Fig.3) are given in table 4, where Z indicates the distancefrom the center of the external emitter, R – radial position.
Table 4. Position of the key points of the MIG shapePoint
number
Z, mm
R, mm
Point
number
Z, mm
R, mm

1

2

3

4

5

1.066
0

0.723
0.562

0.426
0.689

0
0.899

-0.31
0.915

6

7

8

9

10

-0.431
1.158

-1.0
1.17

-1
1.5

2.172
1.5

2.172
2.3

The final stage of numerical simulation requires a more sophisticated physical model [18-20] whichtakes into account such important factors as the thermal velocities distribution and the emitter roughness thatlead to a significant increase in the velocity spread [21]. Besides, the values of the velocity spread specified inTable 3 are not enough to suppress the spurious modes at the fundamental cyclotron harmonic [8]. For this aspread v of about 30–40% is needed. Such values may be ensured by the corresponding manufacturing of anemitter with the prescribed emitter roughness r0 (Fig.4). The velocity spread increases with the emitter surface
roughness (the corresponding formula is given in [12, 20]) and for the average roughness heights r0 = 10 and 20
microns the velocity spread is 27% and 39%, respectively. The specified values of r0 approximately correspondto the maximum and the minimum admissible values of velocity spread. Therefore, in the used numericalsimulation procedure [18] the width of the initial azimuthal velocity distribution function f(v0) was chosen toprovide the specified values of velocity spread for low currents of the electron beams (Iin, Iext0).
The used procedure [18] allowes to find the velocity distribution function in the cavity F(v)=dI/dv andthus to calculate the coefficient KR of reflection from a magnetic mirror for each beam in the operating regime.
According to the results of the numerical simulation of HEBs with a high pitch-factor [22], in order to avoid thebeam instabilities, it is necessary to provide KR less than 2 – 3%. For emitter roughness of 20 microns thereflection coefficient is too high (5 – 6%) for any current of both beams. Concurrently, for a roughness of 10
microns in the operating regime with a current density of 3 A/cm2, the coefficient KR is small enough (1 –

1.5%) to avoid the beam instability. Thus, one can make the conclusion that the manufacturing techniqueproviding the emitter roughness of 10 microns is quite suitable for meeting the two requirements – rather highpitch-factor and simultaneously large enough velocity spread and a small reflection coefficient. The value of KR
can be decreased 2 – 3 times by turning to smaller pitch-factors in both beams close to 1.2.

Fig. 4. Electron beam trajectory near the cathode surface and main parameters for estimation of the velocity spreadcaused by the surface roughness.

The calculations show that increasing currents in each beam shifts the function F(v) simply toward
smaller oscillatory velocities, remaining almost Gaussian for both the internal and external beams. This
indicates that stable HEBs are formed in the operating regimes of the MIG.
6. Conclusion
The design of the double-beam electron gun capable to provide the required beams parameters for both
operating modes TE-15,6 and TE21,4 for the developed 1.2 THz CW gyrotron is proposed. Both analyticalestimations of the MIG shape and further numerical optimization of its geometry were performed. The
sensitivity of the gun to the shift of the gun in the magnetic field and small variations of the anode shape andanode potential are investigated. Special attention was paid to the problem of electrons reflected from themagnetic mirror caused by the emitter roughness. It is shown that the technique providing emitter roughness ofabout 10 microns is quite suitable to ensure both small reflection coefficient from the magnetic mirror and large
enough pitch-factor. The designed gun can provide appropriate parameters for a CW operation of both HEBs.
Additionally, the gun design allows to operate it in both single-beam and double-beam versions simply by
removing or installing additional emitter on the cathode surface and exciting either TE-15,6 or TE21,4 modes (tokeep the frequency when changing the operating mode it is necessary to replace the cavity with the one with asuitable radius). As a result, it is possible to realize even 4 versions of the gyrotrons having minimal, cheap andsimple differences in its design. Such tube has essentially higher flexibility to realize the output power about
several tens of watts at least in CW regime with an extremely high frequency close to 1.2 THz. The
implementation of the presented project will make it possible to create a unique source for DNP/NMR
spectroscopy and a lot of other promising applications.
Acknowledgments
This work supported by RSF grant 19-12-00141.
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Design of a Third-Harmonic 1.2 THz/CW Gyrotron with an Intentionally
Increased Velocity Spread of Electrons
I.Bandurkin1,2, A.Fedotov1.2, M. Glyavin1,*, T. Idehara2, A. Malkin1, V. Manuilov1,2,3, S.Mitsudo2,
A. Sergeev1, S.Sabchevski2,4, A. Tsvetkov1,2, V. Zaslavsky1,3 , I. Zotova1,21Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS
2

3

4

Research Center for Development of Far-Infrared Region,
University of Fukui (FIR FU),

Radiophysical Department of Nizhny Novgorod State University

Institute of Electronics of the Bulgarian Academy of Science (IRE BAS)*

Contributed by the corresponding author M. Glyavin: glyavin@ipfran.ru

Abstract. In this paper, the concept of a CW 1.185 THz (wavelength about 250 μm) gyrotron withan output power of several watts, intended for DNP/NMR spectroscopy applications is presented.
For a 15 T magnetic field provided by a commercially available cryomagnet, the required frequency
can be achieved by operating at the 3rd cyclotron harmonic. Under conditions of extreme density ofthe mode spectrum, we propose using interaction with an electron beam intentionally formed with ahigh (up to 40%) velocity spread as a selection mechanism. This ensures suppression of the mostdangerous parasitic traveling modes at the first and the second cyclotron harmonics, which are very
sensitive to the velocity spread. The main parameters of the gyrotron are determined both using thestart currents analysis and within the framework of a non-stationary self-consistent physical model.
The feasibility of the single-mode 3rd harmonic generation under conditions of mode competition isverified based on 3D PIC (particle-in-cell) simulations. The design of the triode MIG forming two
generating beams with a quality suitable for third harmonic operation is suggested and optimized.
The specific feature of the MIG is the possibility to form either two beams or one beam using thesame electrode geometry and different number of emitting rings. The proposed MIG is not sensitive
to small misalignment and reasonable manufacturing errors. It is shown that it is possible to form
two beams with practically equal and quite high pitch-factors in all range of operating currents andsimultaneously small enough coefficient of reflection from the magnetic mirror despite the large
enough value of the velocity spread.
Keywords — gyrotron; electron beam; THz radiation, harmonic excitation, velocity spread,mode selection, magnetron-injection electron gun, numerical simulation.

1. Introduction
Nowadays, sources of terahertz radiation are in great demand due to their numerous scientific andtechnological applications in physics, chemistry, biology, medicine, etc. Over the last few years, there has beena significant progress in the development of short-wavelength gyrotrons operating at frequencies of 0.4-1 THz[1-5]. The maximum radiation power was achieved in fundamental-harmonic gyrotrons with pulsed magnetic
fields [1-3]. At the same time, for continuous-wave (CW) generation in the THz band, operation at higher-orderharmonics of the cyclotron frequency is inevitable due to the limitation to magnetic field intensity provided by
the available state-of-the-art cryomagnets. However, high harmonic operation leads to complication of the
problem of mode selection in gyrotron cavities, which in the THz band should be significantly oversized.

Currently, a number of methods aimed to improve the situation are under development, which include multibeam gyrotrons [4], interaction with axis-encircling rotating electron beams in the so-called large-orbit
gyrotrons (LOGs) [5,6], the use of complex-profile [7-9] or coaxial cavities [10,11], etc. At the same time, theobvious disadvantages of these methods are caused by difficulties in manufacturing of sophisticated resonators
and/or electron guns. For example, for LOGs, the formation of axis-encircling electron beams requires the useof specific cusp magnetic systems. Partly for this reason, operation at the 3rd cyclotron harmonic in LOGs withthe frequency about 1 THz was realized in compact pulse coils, while CW operation with modern cryomagnets
has been obtained only at the frequencies lower than 0.4 THz [5].
At the same time, the natural mechanism of parasitic mode suppression in the conventional gyrotrons is
associated with the influence of the electron velocity spread which strongly affects the resonance conditions of
the spurious travelling modes. However, as is well-known, the large spread deteriorates the gyrotron optimum
efficiency significantly even for the near-cutoff modes. Thus, the electron guns are usually designed in such a
way as to provide the spread in the orbital velocities not exceeding 15-20%. These values are insufficient forprovision of the selective excitation of the 3rd cyclotron harmonic in conditions of an extremely dense mode
spectrum, as the starting currents of the spurious modes remain far below that of the operating one (see below).
Nevertheless, the situation can be quite different for higher values of the velocity spread, 30 to 40 %; here,
besides the significant increase in the starting currents of the spurious 1st and 2nd harmonic traveling modes, thestarting current of the operating near-cutoff 3rd harmonic mode is reduced. This latter effect [12-14] can be
explained by the influence of “slow” electron fractions with smaller axial velocities which contribute more to
the electron susceptibility due to two factors: first, they interact with the cavity field longer; second, theseparticles have higher transverse velocity. As a result, for near-cutoff modes, this contribution is larger than thenegative contribution of the electrons with larger axial velocities and thus the total susceptibility is increased.
Therefore, using an electron beam with a large velocity spread one can provide conditions when the
excitation zone of the 3rd harmonic near-cutoff mode is not masked by zones of spurious modes excited at the
1st and the 2nd cyclotron harmonics, assuming these latter modes are traveling. In this paper, we use such an
approach for development of a 1.185 THz CW gyrotron intended for spectroscopic applications. In Section II,
basic parameters of the gyrotron are determined based on an analysis of the starting currents as well as within
the framework of a self-consistent non-stationary multimode model in which the difference in the interaction(transit) time for “slow” and “fast” electron fractions is taken into account. In Section III, the feasibility ofsingle-mode 3rd harmonic generation is verified based on 3D PIC (particle-in-cell) simulations using CSTSTUDIO SUITE [15].
2. Analysis of the starting currents and estimations of the output Parameters
In designing a gyrotron, the first thing to do is to choose an operating mode based on the parameters of the
gyrotron cavity determined by the technological properties of state-of-the-art milling machines. These arecapable of manufacturing relatively long (tens of millimeters) cylindrical cavities with diameters of 2R ~ 2.5  3
mm with a sufficient precision (inaccuracy less than 0.01  ). Since the mode competition problem becomes
more severe with an increasing of R , the inner diameter of the cavity was chosen close to the minimum
admissible value 2R  3 mm. For an operation at a quasi-cutoff frequency c , the condition c c   R should
be fulfilled, where  is the eigenvalue of a TEm,q mode of a cylindrical waveguide. Thus, for an operating
frequency of 1.2 THz, one should choose a mode with   37 . The above considerations allow us to propose theTE15,6 mode as an operating one for which the maximum value of the coupling factor is reached for a beam
injection radius of 0.84 mm. In this case, the most “dangerous” parasitic modes are, at the 1 st cyclotron
harmonic, TE6,2 and, at the 2nd cyclotron harmonic, TE3,7 , TE1,8 , TE8,5 ; among these, only TE8,5 is quasicutoff.
Calculations of the starting current were performed within the framework of the single-mode stationary model
based on 1D hyperbolic “non-uniform string” equation [16.17] for the field amplitude and averaged over the
cyclotron period linearized equations for the motion of the electrons. The distribution of the beam particles over
the transverse velocities at the cavity entrance was assumed to be Gaussian with the width at the level e1 taken
for the velocity spread value. The operating zones of the indicated modes shown in Fig. 1 were found for the
gyrotron cavity length of 15 mm and the following parameters of the driving electron beam: electron energy 30
keV and mean pitch-factor 1.3. One can see that at zero velocity spread (Fig. 1a) and at the velocity spread of
20% typical for conventional gyrotrons (Fig. 1b), there is no chance of selective excitation of the operating 3rd

harmonic mode (blue line) with a minimum starting current of 1.5 A, due to the fact that the starting current of
the 1st harmonic spurious mode TE6,2 (red line) is significantly lower. At the same time, the situation becomesquite different for a sufficiently large velocity spread of 40% (Fig. 1c). In this case, the minimum starting
current of the operating TE15,6 mode is reduced to 0.5 A, while the starting current of the most “dangerous”
fundamental harmonic mode increases significantly up to 2-2.5 A.

Fig.1 Starting currents of modes interacting at the fundamental (dotted), second (dashed), and third (solid)
cyclotron harmonics for the designed 1.2 THz CW gyrotron: (a) – zero velocity spread in the electron beam; (b)– 20% spread, (c) – 40% spread. The red stars show the zone where selective excitation of the operating mode
was obtained in 3D PIC simulations.
As mentioned above, this is caused by the influence of “slow” electron fractions with a longer transit time. For
the second-harmonic spurious mode the situation is similar: the starting currents of the travelling TE3,7 andTE1,8 modes increase significantly, while the excitation zone of the near-cutoff TE8,5 mode is slightly shifted

down as is for the operating mode. Nevertheless, one can see that for magnetic fields 14.93-14.98 T, a zone

exists with no competing modes for the 3rd harmonic operating TE15,6 mode. This effect can be observed for atleast 10-15% parameter variation (that is, pitch 1.2-1.4 and length of the resonator 15-17 mm).
In the simulations, the following physical model has been used:i 2 an
Z

2

 sn

an
  i n  in  Z   n  an 
2  i m  sn 

i

e n
I n 0||s ||  p0  || dp

42

|| g 2 p

   p0  p

0

dpd 
,

(1)





p
2
2

 ip p  p0 Z || 4  || i  ann||

 p* 
||sn 1 i  m  s 
n n

e

.

Here, an is the normalized amplitude of the n-th mode TEmn ,qn excited at the cyclotron harmonic with a number
sn , p is the normalized complex transverse momentum of the electrons,   g 4 t 8||2 , Z  2  g z 2||c ,||,   v||,  c are the mean values of the normalized longitudinal and transverse velocities of the electron beamwith a velocity spread, g   || is the mean pitch-factor,  n  8||2 sn sn g  cn cn 4 is the cyclotron
resonance detuning for the n-th mode with a cut-off frequency cn in the regular part of a smoothly tapered
gyrotron cavity, g  eB0 me c  is an unperturbed relativistic gyro-frequency,   1  eU me c 2 is the relativistic
factor, U is the accelerating voltage, me is the electron’s rest mass,2 sn  4 

I n  64eIb ||
me c3



2
J m2  s   n Rb 

n n
.

  2  m2 J 2   
2
s
!
n 

n
n mn n s snsn3  n snAn additional analysis of the possibility of single-mode excitation at the 3rd cyclotron harmonics under theconditions of mode competition is carried out on the basis of a non-linear theory within which the process ofelectron-wave interaction is described by the following self-consistent system of equations (cf. [18]) are thenormalized current parameters, Rb is an injection radius of a tubular electron beam with current I b ,  n is the
eigenvalue of the n-th mode. Function   p0  is defined as an electron transverse velocity distribution function(further assumed to be Gaussian), || ||  g 2  1  g 2 p0 2 ,  n is the parameter of Ohmic losses proportional to

the skin depth, functions n  Z   8||2 cn  cn  Z  4 cn describe the geometrical detunings in a gyrotron cavity
with profile R  z  , cn  Z    n c R  z  . Note, that the term (|| g 2 4|| ) p  in the motion equations permits us totake into account the finiteness of the particle transit time [19], which is different for different electron fractionsof the electron beam with non-zero velocity spread. Thus, based on the developed approach, the influence of“slow” fractions can be directly taken into account using such non-stationary model. For comparison, theprevious non-stationary gyrotron theory taking into account the velocity spread (see, for example, [18]) was
developed under the assumption that the electron transit time is much shorter than the cavity decay time.
Actually, it meant that in the simulations, the transit time was considered to be zero for all electron fractions.
In order to introduce appropriate boundary conditions, we assume that at the input cross section Z  0 , theelectrons are uniformly distributed over the cyclotron rotation phases p  Z  0   p0 ei0 , 0  0, 2  . For theamplitude of electromagnetic field standard non-reflection boundary conditions can be applied on the edges of
the interaction space (cf. [20]):is 10 1  e n n   an  , Z an  , Z  0  d   0,Zisn 0  
Z 0
,
(2)
1 L
 isn n   a  , Z 
1 enan  , Z  L  d   0,
isn 0  

Z

Z L

whereL  2 H l 2||cisthe normalized length

of

the

gyrotroncavity,0n   n  n  Z  0    n,

 nL   n  n  Z  L   n .

Based on Eqs. (2), we carry out simulations, in which the competition of the operating 3d harmonic TE15,6
mode with the most dangerous modes ( TE6,2 at the 1st cyclotron harmonic and TE8,5 at the 2nd cyclotron
harmonic) is taken into account. The results of the simulations for the beam current of 0.7 A are presented in
Fig.2.
One can see that, according to both linear and non-linear analysis, for zero velocity spread, the excitation of
the 1st harmonic travelling mode with five axial variations of the field along the gyrotron cavity (Fig.2, left
column) takes place (radiation power is 140 W). At the same time, introduction of the large velocity spreadallows us to successfully suppress the excitation of both parasitic modes. As a result, we obtain selective singlemode excitation at the 3d cyclotron harmonic with one axial variation of the field (Fig.2, right column). Thisapproach allows us to estimate the output radiation power which, according to the simulations, can reach 10 W.
Note that the starting currents can also be found from Eqs. (1)-(2) by linearization and replacement of  
terms with i , where   8||2    sn g  g 4 . However, in Eq. (1) we used the parabolic dispersion
approximation valid near the exact cutoff frequency; thus the starting currents presented in Fig.1 are moreaccurate as they are found based on exact hyperbolic dispersion equations.

Fig.2 Results of the simulations within the framework of the averaged approach (1) for the operating current of
0.7 A. Oscillations onset (a) and the longitudinal profile of the field amplitude in CW regime (b) for zero
velocity spread (left column) and large spread of 40% (right column). ( B0 = 14.92 T)

3. Results of 3D PIC simulations
The obtained results have been confirmed by the 3D PIC simulations performed using CST Studio Suite.
Such an approach allows us to take into account the competition of all the modes in the gyrotron cavity.
However, for an extremely high operating frequency (over 1 THz) and excitation of the 3d cyclotron harmonic,
this requires significant computer resources compared to simulations within the framework of the averaged
equations approach (1). For the parameters chosen above, the simulation was run with approximately 7×107
hexahedral mesh cells. The total number of macroparticles in the interaction space reached 3×10 6 injected from
128 different injection points. The simulations were carried out using a multiprocessor computer with 16
parallel processors and 2 GPUs. Forty nanosecond long simulation (which is sufficient for the onset of a steadystate regime) required approximately 100 hours of computational time. In general, the performed simulation
resembles the one performed in [21]. However, unlike the simulation of gyrotrons at the fundamental harmonicof the gyrofrequency, the study of the interaction processes at higher cyclotron harmonics requires an increasein the accuracy of the calculations. Correct description of a rotating operating mode calls for a substantial
increase in the number of cells. In addition, the analysis of gyrotron operation at higher harmonics requires afairly accurate determination of the oscillatory velocity spread and, accordingly, a significantly larger numberof macro-particles.

The rsults of the simulations are presented in Fig.3 and 4. The conductivity of copper walls ~ 5.8 107 S/m wastaken into account for proper calculation of the Ohmic losses. For zero spread, an excitation of the 1st harmonic
TE6,2 mode is observed (Fig.3). At the same time, for a spread of 40%, selective excitation of TE15,6 mode atthe 3rd cyclotron harmonic with operating frequency of 1.185 THz takes place (Fig.4). The output power in PIC
simulations is about 6 W, which is in a good agreement with the results obtained within the framework of theaveraged approach. Note also that operating regimes with the power of several watts were observed for zone ofmagnetic fields from 14.93 to 14.96 T, which is close to theoretical prediction (see Fig.1c).

Fig.3 Results of 3D PIC simulations in the case of zero velocity spread: (a) output power vs time; (b) radiation
spectrum; (c), (d) axial and transverse field structures corresponding to an excitation of TE6,2 mode at thefundamental cyclotron harmonic. ( B0 = 14.94 T, U = 30 kV, I b = 0.7 A)

Fig.4 The same as in Fig.3 for velocity spread of 40%, when selective excitation of TE15,6 mode at the 3d
cyclotron harmonic takes place. ( B0 = 14.94 T, U = 30 kV, I b = 0.7 A)

4. Selection of the injection radius of the electron beam
The coupling factors for TE-15,6 or TE21,4 modes are presented in Figure 5.

Fig. 5. Coupling of the electron beam to the eigenmodes of a cylindrical cavity vs. the electron beam injection
radius Rbeam: TE+21,4 (harmonic number s = 3), TE-15,6 (s = 3), TE8,5(s = 2).Cavity radius Rcavity is equal to1.488 mm.
Below, the two versions of a gyrotron are preliminary considered: a conventional single-beam gyrotron and adouble-beam gyrotron. In the first case, for an injection radius of 0.85 mm, the coupling factor for both
operating modes is significantly higher than for the parasitic ones TE±8,5. In the second case, there is also theexternal helical electron beam (HEB) with a radius Rbeam = 1.07 mm. This beam has a fairly strong coupling to
the parasitic mode. However, its usage together with the main internal HEB does not violate the selective
excitation of the operating mode (at a reasonable value of the current of this beam) and makes it possible toincrease the total current, allowing increasing the output power of the tube.
5. Admissible spread of the electron beam injection
One of the parameters that must be known before starting the design of the MIG is the spread of the guiding
centers in the HEB. It defines, to some extent, the electron beam current and possibility to manufacture theemitter ring with good enough accuracy. We estimated the minimum values of the starting currents in Ist min (B)curve, where B is the intensity of the magnetic field, for one of the operating modes, TE15,6, and for the mainparasitic mode TE8,5 as a function of the thickness Rbeam of the electron beam. In these calculations, weconsidered the case of a single HEB with a radius Rbeam = 0.85 mm.
For the simplest model with a fixed longitudinal structure of the microwave field f(z) = sin(πz/L) (where
L is the effective length of the gyrotron cavity), in case when the electron beam has a finite thickness Rbeam,
the starting current can be calculated using a generalization of the well-known formula [17, 22]: R

R

I st  ( ) 

/2

beam
beam
1

G
m , p ( R) dR  1 ,Rbeam Rbeam  Rbeam / 22eQL 2  20s  2  s s  d  1  cos ( )   s    s  ,32
mc  0||0  2 s!  d  [1  ( /  ) 2 ]2I st min (Rbeam )  min I st ( H ) ,H

where θ = (ω–sωc)L/v|| is the transit angle, ωc = eH0/mcγ0 is the unperturbed cyclotron frequency,
γ0 = 1 + U0[kV]/511 is the relativistic mass factor, U0 is the accelerating voltage, Q is the quality factor of thegyrotron cavity, β⊥,|| = v⊥,||/c are the normalized transverse and longitudinal velocities, μ= πgβ⊥0L/λ is thenormalized interaction length, and λ is the radiation wavelength.
The results of the calculation are shown in Fig. 6.
With an increase in the HEB thickness, the minimum value of the starting current for the spurious TE8,5
modes dramatically decreases (dashed and dash-dotted lines in the figure), and simultaneously, the starting
current of the operating one TE-15,6 rapidly increases (Fig. 6). Thus, it seems reasonable to choose a beam
thickness of about /5 following the compromise: on the one hand, a further decrease in the beam thickness
does not significantly improve the situation; on the other hand, this value seems realistic from the point of viewof the implementation of the electron-optical system.
6. Preliminary adiabatic estimation of the MIG parameters
First, we consider a gyrotron based on the same magnetic system as in the project of 0.79 THz double-beamgyrotron operating at the second cyclotron harmonic [23]. To ensure high coupling of the two beams with RF
field and good enough gyrotron efficiency the following HEBs parameters were chosen: Rin = 0.854 mm (0.85mm), Rext = 1.065 mm (1.07 mm), gin =gext = 1.3, vin =vext  30 – 40%, Iin , Iext  0.8 A. Here the indexes“in” and “ext” correspond to internal and external beams, respectively and the values in brackets correspond to
the TE21,4 mode. The spreads of the guiding centers Rin and Rext should be less than /5. Here Rin, Rext are
partial beams radii, gin, gext – pitch-factors, Iin, Iext – corresponding currents of each beam.
The specified values of the injection radii for both operating modes are very close: the difference incorresponding injection radius is less than /50, i.e. 10 times smaller than the admissible value of the guiding
centers spread. This allows to design an universal scheme of a double-beam MIG suitable for utilization in thesame gyrotron operating at both specified above modes simply by replacing the corresponding cavity inside thetube (to keep the frequency value of about 1.185 THz for the operating mode TE21,4 the cavity radius must be
equal to 1.492 mm).

Fig. 6. Minimum value of the starting current Ist min as a function of the thickness of the electron beam for theoperating mode TE-15,6 and for the parasitic one TE8,5, expressed in wavelengths /Rbeam. The same value of/Rbeam corresponds to different values of the magnetic field strength.
Relatively low value of the accelerating (cathode) voltage U0 should be preferred in order to simplify the
gyrotron power supply system [24]. On the other hand, to satisfy the cyclotron resonance condition:  3с  3 

2  28 H [T ]for a fixed maximum value of the magnetic field intensity H (which is not higher than 15 T) we need to limit
the value of the accelerating potential to approximately 32 kV. Hence, below we consider a version of thebeam-shaping system with a total accelerating voltage of 30 kV and a maximum total beam current of 3 A (i.e.
in the two HEBs), which are estimated to guarantee an output power of about a hundred watts at least. For a
more flexible control of the parameters of the partial HEBs, we consider a triode scheme of the MIG with ananode voltage Ua ≈ 12 kV.
The preliminary analytical estimation of the operational regime and the MIG dimensions was performed
based on the adiabatic theory of HEB formation system [25]. The laminar electron beam was suggested, so themagnetic-field line to the emitter angle  must be 25. The initial gyrotron parameters, which were further
used for analytical estimations, are summarized in Table1, preliminary data of MIG estimations are presented inTable 2.
Table 1.Gyrotron parameters in the interaction space.
Wavelength 
Operating magnetic field Bo
Accelerating voltage UoFirst-anode potential Ua
Beam radii in a cavity Rext(external beam)
and Rin (internal beam) TE-15,6 mode
TE21,4 mode
Operating beam currents Iext and Iin
Pitch factors g1 and g2
Magnetic-field line toemitter surface angle 0.250 mm
14.9 T
30 kV
12 kV
1.065 mm, 0.854 mm
1.070 mm, 0.850 mm
1.7 A and 1.3 A
1.3
25

Table 2.Basic design parameters of the beam shaping system.
Cathode electric field Ec
Spread of guiding centers in the cavity,Ro(both beams)
Emitter width L (for each beam)
Current density jc(for both beams)
Ratio tjof thecurrent to the Langmuircurrent (for both beams)
Magnetic field compression
 (external and internal beams)
Emitter inclination  to the axis (external beam)
Cathode radius Rc2(external beam)
Anode radius Ra2(external beam)
Emitter inclination  to the axis (internal beam)
Cathode radius Rc1(internal beam)
Anode radius Rа1(internal beam)

2.36 kV/mm

/5
1.0 mm
3.0 A/cm2
0.25
71.4 and 69.130
9.0 mm
14.6 mm
25
7.1 mm13.5 mm

It is important to note that the chosen emitter width (1 mm for both beams) satisfies the two formulated
above requirements. On the one hand, such width allows to manufacture the emitter ring using the existing
technology (manufacturing of smaller ring is a much more complicated task). On the other hand, the restriction
imposed by the admissible value of the spread of the guiding centers in the cavity is taken into account as well.
7. Results of the electron trajectory analysis of a double-beam MIG1
The second step of the MIG optimization is, as usual, the numerical simulation of the beam properties andoptimization of the gun shape.
1

This section repeats almost verbatim the results of the preceding paper in this Newsletter for completeness, consistency andindependence of both articles.

In order to simplify the manufacturing of the electron gun and the gyrotron tube itself and to make it cheaper,the distance from the gun to the cavity was kept close to the distance (570 mm) used in the previous version of
double-beam gyrotron [23] operating on the second cyclotron harmonic. Besides, the shape of the second anodewas preserved the same as well.
The optimization was done using the two-dimensional software EPOS [26]. The final MIG geometry is
shown in Fig. 7. The first anode is parallel to the tube axis. The beams parameters calculated according to themodel without the initial velocity distribution (such model usually is used during the first step of the
optimization) are shown in Table 3. Both beams have very close pitch-factors and smooth dependence of theirproperties on the operating current.
The calculations show also that the velocity spread  v practically does not depend on any kind of the gungeometry deviation caused by a system misalignment or a thermal deformation of the electrodes for both theinternal and external electron beams: it varies by no more than on (0.3 – 1.0)%. Similarly, the pitch factor
varies by no more than 0.12 when a longitudinal shift of the magnetic system is in the range of 2 mm. The
sensitivity of the pitch-factor to the radial shift of the first anode is significantly higher, especially for theexternal beam due to the rather small anode-cathode distance and can reach 0.3. The latter effect, however,can easily be counterbalanced by small variations in the anode potential Ua. Due to the cylindrical form of thefirst anode the gun is not sensitive to the longitudinal shift of the first anode.
Table 3. Calculated beams parameters in the nominal regime for an anode voltage Ua = 11.73 kV
internal beamjk, A/cm
I, Ag
1.00.44 1.46
1.5
0.65 1.40
2.0
0.87 1.34
3
1.31 1.24

v
0.03
0.04
0.05
0.08

2

jk, A/cm
1.0
1.5
2.0
3

external beam
I, A
g
0.56
1.44
0.84
1.39
1.12
1.34
1.68
1.24

2

v
0.04
0.05
0.07
0.10

Fig.7. The shape of the electrodes and trajectories of the electrons in the first anode region of double-beam
MIG. The anode potential is 11.73 kV.
The key points of the optimized MIG geometry (Fig.7) are given in Table 4, where Z indicate the distancemeasured from the center of the external emitter, R being the radial position.
Table 4. Position of the key points of the MIG shapePoint
number
Z, mm
R, mm
Point
number
Z, mm
R, mm

1

2

3

4

5

1.066
0

0.723
0.562

0.426
0.689

0
0.899

-0.31
0.915

6

7

8

9

10

-0.431
1.158

-1.0
1.17

-1
1.5

2.172
1.5

2.172
2.3

The final stage of the numerical simulation has been performed using a more sophisticated physical model[25-27] which takes into account such important factors as the thermal velocities of the electrons and theroughness of the emitter surface both leading to a significant increase in the velocity spread [28]. Besides, thespecified in Table3 values of the velocity spread are not enough to suppress the excitation of spurious modes at
the fundamental cyclotron harmonic [29]. Such suppression is possible only at high enough values of v
reaching 30–40%. They can be ensured by the corresponding manufacturing of the emitter with a prescribed(suitable) emitter roughness r0 (Fig.8). The velocity spread increases with the emitter surface roughness (thecorresponding formula is given in [25, 26]) and for the average roughness height r0 = 10 and 20 microns thevelocity spread is 27% and 39%, respectively. The specified values of r0 approximately correspond to the
maximum and the minimum admissible values of the velocity spread. Therefore, in the used numericalsimulation procedure [26] the width of the initial azimuthal velocity distribution function f(v0) was chosen toprovide the specified values of the velocity spread for low currents of the electron beams (Iin, Iext0).
This procedure [26] allows to find the velocity distribution function in the cavity F(v)=dI/dv and thus tocalculate the coefficient of reflection KR from the magnetic mirror for each beam in the operating regime.
According to the results of numerical simulation of HEBs with high pitch-factor [30], to avoid the beam
instabilities, it is necessary to keep KR less than 2 – 3%. For an emitter roughness of 20 microns the reflection
coefficient is too high (5 – 6%) for any current in both beams. Concurrently, for a roughness of 10 microns in
the operating regime with a current density of 3 A/cm2, the coefficient KR is small enough (1 – 1.5%) to avoid
the beam instability. Thus, one can make the conclusion that the manufacturing technique providing the emitterroughness of 10 microns is quite suitable for meeting the two requirements, namely a rather high pitch-factor
and simultaneously a large enough velocity spread and a small reflection coefficient. The value of KR can be
decreased 2 – 3 times by turning to smaller pitch-factors in both beams close to 1.2.

Fig. 8. Electron beam trajectory near the cathode surface and main parameters used for evaluation of thevelocity spread caused by the surface roughness
The calculations show that increasing currents in each beam shifts the function F(v) simply toward smaller
oscillatory velocities, remaining almost Gaussian for both the internal and external beams. This indicates thatstable HEBs are formed in the operating regimes of the MIG.
8. Conclusions
Using independent approaches, we have demonstrated the possibility of improvement of the mode selectivity
for the case of excitation of a high-order cyclotron harmonic in THz-range gyrotrons by deliberately
introducing an appropriate (and large enough) velocity spread in the driving electron beam. Based on thesefindings, a concept of a novel CW gyrotron capable of operation at the 3rd cyclotron harmonic with thefrequency of about 1.2 THz has been proposed. The values of the required velocity spread were determined.
The results of numerical simulations show that in order to suppress the spurious modes on the 1st and 2nd
cyclotron harmonics, it is necessary to use helical electron beams with velocity spread of about 35-40%. The
specified velocity spread can be obtained by using an emitter sponge with a suitable grain size (emitterroughness).
The design of the double-beam electron gun capable of providing the required beams parameters for two
operating modes, namely TE-15,6 and TE21,4 has been proposed. The gun design allows to operate both in singlebeam and double-beam versions simply by removing or installing additional emitter on the cathode surface. The

roughness of the emitter can be controlled during the manufacturing of the cathode. For LaB6 cathodes, 30% or
40% velocity spread can be obtained for the grain size of about 10 or 20 micrometer, correspondingly.
It is worth noting that despite the fairly low efficiency, the proposed scheme of high-harmonic THz band
generation appears to be very promising and simple in implementation. The output power of the order ofseveral watts significantly exceeds the power provided by the classical electronic devices in this range (forexample, BWOs), and is sufficient for many spectroscopic applications, including DNP/NMR spectroscopy.
References[1] T. Idehara, H. Tsuchiya, O. Watanabe, La Agusu and S. Mitsudo, “The First Experiment of a THz Gyrotron
with a Pulse Magnet,” Int. J. Infrared & Millimeter Waves, vol. 27, n. 2 (2006) 319-331. DOI:10.1007/s10762006-9084-9.
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Denisov, D. Kashin, G .Rogers, C.A. Romero-Talamas, R. Pu, A.G. Shkvarunetz, and G.S.Nusinovich"Experimental Study of the Pulsed Terahertz Gyrotron with Record-Breaking Power and Efficiency
Parameters," Radiophys. Quantum Electr., vol 56 (2014) 497–507. DOI:10.1007/s11141-014-9454-4.
[4] T. Idehara, M. Glyavin, A. Kuleshov, S. Sabchevski, V. Manuilov, V. Zaslavsly, I. Zotova and A. Sedov,“A Novel THz-Band Double-Beam Gyrotron for High-Field DNP-NMR Spectroscopy,” Rev. Sci. Instr., vol.
88, n. 9 (2017) 094708. DOI:10.1063/1.4997994.
[5] V.L. Bratman, Yu.K. Kalynov, and V.N. Manuilov, “Large-Orbit Gyrotron Operation in the Terahertz
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[6] Yu.K. Kalynov, V.N. Manuilov, A.Sh. Fiks, and N.A. Zavolskiy “Powerful continuous-wave sub-terahertz
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[7] I. Bandurkin, M. Glyavin, S. Kuzikov, P. Makhalov, I. Osharin, and A. Savilov. “Method of providing thehigh cyclotron harmonic operation selectivity in a gyrotron with spatially developed operating mode,” IEEE
Trans. on Electron Devices, vol. 64, n. 9 (2017) 3893-3897. DOI:10.1109/TED.2017.2731982.
[8] M.M. Melnikova, A.G. Rozhnev, N.M. Ryskin, Y. Tatematsu, M. Fukunari, Y. Yamaguchi, T. Saito“Electromagnetic Modeling of a Complex-Cavity Resonator for the 0.4-THz Second-Harmonic FrequencyTunable Gyrotron,” IEEE Transactions on Electron Devices, vol. 64, n. 12 (2016) 5141-5146.
DOI:10.1109/TED.2017.2764874.
[9] S. Yu, Q. Zhao, T. Zhang, Y. Yang, Y. Zhang, and Z. Wang. “The theoretical investigation and design on
0.42 THz gyrotron with complex cavity,” Terahertz Science and Technology, vol. 9, n. 4 (2016) 149-165.
DOI:10.11906/TST.149-165.2016.12.15.
[10] V. I. Shcherbinin, Y. K. Moskvitina, K. A. Avramidis, and J. Jelonnek, “Improved mode selection incoaxial cavities for subterahertz second-harmonic gyrotrons,” IEEE Trans. Electron Devices, vol. 67, n. 7(2020) 2933-2939. DOI:10.1109/TED.2020.2996179.
[11] V. I. Shcherbinin, V. I. Tkachenko, K. A. Avramidis, and J. Jelonnek, “Coaxial cavity with stepped innerconductor for a sub-terahertz second-harmonic gyrotron with broadband continuous frequency tuning,” IEEE
Trans. Electron Devices, vol. 66, n. 12 (2019) 5313-5320. DOI:10.1109/TED.2019.2944647.
[12] I.I. Antakov, V.S. Ergakov, E.V. Zasypkin, and E.V. Sokolov, “Starting conditions of a CRM monotron in
the presence of scatter of the velocities of the electrons,” Radioph.&Quant. Electr., vol. 20, n. 4 (1977) 413418. DOI:10.1007/BF01033931.
[13] M. Yeddulla, G.S. Nusinovich, and T.M. Antonsen, "Start Currents in an Overmoded Gyrotron”, Phys.
Plasmas 10, 4513-4520 (2003); DOI:10.1063/1.1618777.
[14] G.F. Brand, P.W. Fekete, K. Hong, K.J. Moore, and T. Idehara, “Operation of a tunable gyrotron at thesecond harmonic of the electron cyclotron frequency,” Int. J. Electronics, vol. 68, n. 6 (1990) 1099-1111.
[15] https://www.3ds.com/products-services/simulia/products/cst-studio-suite/[16] N.A. Zavolsky, V.E. Zapevalov, and M.A. Moiseev, “Efficiency enchamcement of the relativistic
gyrotron,” Radiophys.and Quant. Electr., vol. 44, n. 4 (2001) 318.
[17] G.S.Nusinovich, “Introduction to Physics of Gyrotons”, J. Hopkins Univ. Press, Baltimore-London, 2004.

[18] O. Dumbrajs , T. Saito , Y. Tatematsu , and Y. Yamaguchi, “Influence of the Electron Velocity Spread andthe Beam Width on the Efficiency and Mode Competition in the High-Power Pulsed Gyrotron for 300 GHz
Band Collective Thomson Scattering Diagnostics in the Large Helical Device,” Phys. Plasmas vol. 23 (2016)093109. DOI:10.1063/1.4962575.
[19] N. S. Ginzburg, A. S. Sergeev, and I. V. Zotova, “Time-domain self-consistent theory of frequencylocking regimes in gyrotrons with low-Q resonators,” Phys. Plasmas, vol. 22 (2015) 033101.
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[20] N.S. Ginzburg, G.S. Nusinovich, N.A. Zavolsky, “Theory of non-stationary processes in gyrotrons withlow Q resonators,” Int. J. of Electronics, vol. 61 (1986) 881.
[21] V.Zaslavsky, N.Ginzburg, M.Glyavin, I.Zheleznov, I.Zotova, "Three-dimensional particle-in-cell modelingof terahertz gyrotrons with cylindrical and planar configurations of the interaction space," Phys. Plasmas, vol. 20(2013) 043103.
[22] O. Dumbrajs, T. Idehara, T. Saito, and Y. Tatematsu, “Calculations of Starting Currents and Frequencies inFrequency-Tunable Gyrotrons,” Jpn. J. Appl. Phys., vol. 51 (2012) 126601.
[23] V.N. Manuilov, M.Yu. Glyavin, A.S. Sedov, V.Yu. Zaslavsky, T. Idehara, “Design of a Second Harmonic
Double-Beam Continuous Wave Gyrotron with Operating Frequency of 0.79 THz,” J. Infrared Millim.
Terahertz Waves, vol. 36, n. 12 (2015) 1164-1175.
[24] M.Glyavin, N.Zavolsky, A.Sedov, G.Nusinovich, “Low voltage gyrotrons,” Physics of plasmas, vol. 20, n.
3 (2013) 033103.
[25] Sh.E. Tsimring, Electron Beams and Microwave Vacuum Electronics. Hoboken, NJ: John Wiley & Sons.
Inc. (2007)[26] P.V. Krivosheev, V.K. Lygin,V.N. Manuilov, Sh.E. Tsimring, “Numerical Simulation Models of Forming
Systems of Intense Gyrotron Helical Electron Beams,” Int. J. Infrared Milli. Waves, vol. 22 (2001) 1119-1145.
[27] V.K. Lygin, “Numerical simulation of intense helical electron beams with the calculation of the velocity
distribution functions,” Int. J. Infrared Milli. Waves, vol. 16 (1995) 363-376.
[28] Sh.E. Tsimring, “On the spread of velocities in helical electron beams,” Radiophys. Quantum Electron,
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[29] M. Yeddulla, G.S. Nusinovich, T.M. Antonsen, “Start currents in an overmoded gyrotron,” Phys. Plasmas,
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[30] V.N. Manuilov, “Numerical simulation of low-frequency oscillations of the space charge and potential in
the electron-optical system of a gyrotron,” Radiophys. Quantum Electron., vol. 49 (2006) 786-792.
DOI:10.1007/s11141-006-0113-2.

More detail on the project:
1. V.N. Manuilov, A.I. Tsvetkov, M.Yu. Glyavin, S. Mitsudo, T. Idehara, I.V. Zotova, “Universal Electron
Gun Design for a CW Third Harmonic Gyrotron with an Operating Frequency over 1 THz,” Journal of
Infrared, Millimeter, and Terahertz Waves, vol. 41 (2020) 1121–1130. DOI: 10.1007/s10762-02000702-5.
2. I. Bandurkin, M. Glyavin, T. Idehara, A. Malkin, V. Manuilov, A. Sergeev, A. Tsvetkov, V. Zaslavsky ,I. Zotova, “Development of Third-Harmonic 1.2-THz Gyrotron With Intentionally Increased Velocity
Spread of Electrons,” IEEE Trans Electronic Devices, vol. 67, n. 10 (2020) 1557-9646.
DOI:10.1109/TED.2020.3012524.

FORTHCOMING EVENTS (UPDATED ANNOUNCEMENTS)

Announcement by the organizers: “We regret to inform you that because of the significant health risks andtransportation disruptions associated with the COVID-19 pandemic we are forced to postpone the 11th
International Workshop “Strong Microwaves and Terahertz Waves: Sources and Applications” until
summer 2021.
We will inform you about the planned dates for the Workshop as soon as they are available. Please visit thewebsite of the Workshop.
Thank you for your interest in our Workshop and hope to see all of you in Nizhny Novgorod next summer.”

The 8th International Workshop on Far-Infrared Technologies(IW-FIRT 2021)(March 8-9, 2021, University of Fukui, Fukui, Japan)
The first International Workshop on Far-Infrared Technologies (IW-FIRT) was held in 1999 as a celebration
event for establishing FIR FU, and the second IW-FIRT was held in 2002 as a part of the Fukui University
International Congress to celebrate the 50th anniversary of our university. The third IW-FIRT was held in 2010,
eight years after the second IW-FIRT, to commemorate the 10th anniversary of the foundation of FIR UF. The
fourth, fifth, and sixth IW-FIRT were held in 2012, 2014, 2017, and 2019, successively, every few years. In
these workshops it was aimed to discuss the recent developments and future directions of far-infrared andterahertz science and technologies with a special emphasis on high power radiation sources in this frequency
region and their applications. We feel that it is the time to organize the next IW-FIRT to update our knowledge
and understanding in this rapidly developing field. Therefore, we organize the 8th International Workshop on
Far-Infrared Technologies (IW-FIRT 2021). In view of the pandemic of COVID-19 the Workshop will beheld on 8 and 9 March 2021 online via Zoom. For more detail please visit the website of the Workshop.

SPECIAL JOURNAL ISSUES IN THE FIELD OF THZ SCIENCESpecial Issue "Design, Technologies and Applications of High Power Vacuum Electronic Devices fromMicrowave to THz Band". For more detail, please follow the link.

Special Issue "Terahertz Optical Elements: Science and Technology". For more detail, please follow
the link.

PERSONALIA
Academician Professor Alexander Litvak at 80

On November 17, 2020, Alexander Grigorievich Litvak turns 80 - an outstanding physicist, academicianof the Russian Academy of Sciences, member of the Presidium of the Russian Academy of Sciences (RAS),
member of the Bureau of the Physical Sciences Division of the Russian Academy of Sciences, scientificdirector of the Federal Research Center of the Institute of Applied Physics of the Russian Academy of Sciences(IAP RAS), Doctor of Phys.-Math. Sciences, Professor.
In 1962, A.G. Litvak graduated from the radiophysical faculty of the Gorky State University named
after N.I. Lobachevsky and entered graduate school under the guidance of Professor M.A. Miller. In 1967, A.
Litvak defended his Ph.D. thesis "Some questions of the theory of nonlinear electromagnetic phenomena inplasma", and in 1977 - the thesis "Self-action and interaction of electromagnetic waves in plasma" for the
degree of Doctor of Phys.-Math. Sciences. Since 1977, in the newly organized Institute of Applied Physics of
the Academy of Sciences of the USSR, A.G. Litvak has consistently headed the sector, laboratory, and plasma
physics department. In 1988, A.G. Litvak became the head of the Department of Plasma Physics and HighPower Electronics, and since 2003, for 12 years, he was Director of the Institute of Applied Physics of theRussian Academy of Sciences, and since May 2015 a Scientific Director of the Institute. In 2016, Academician
Alexander Litvak was awarded the title "Honorary Professor of the Lobachevsky State University of N.
Novgorod.
A. G. Litvak is a prominent, widely recognized specialist in the field of plasma physics, physicalelectronics and radiophysics. The scientific activity of A.G. Litvak covers a wide range of problems, such as theinteraction of powerful electromagnetic radiation with matter, the development and creation of dense plasma
sources, the development of microwave methods for heating of plasma in controlled thermonuclear fusion
installations, the development of powerful microwave radiation sources and their use for creating newtechnologies.
Already at the first stage of his scientific activity, A.G. Litvak carried out fundamental work on
nonlinear electrodynamics of plasma and condensed matter. He formulated averaged dynamic equations forplasma and field, which made it possible to study from a unified standpoint the processes of self-focusing andstimulated scattering of electromagnetic waves in isotropic and magnetoactive plasmas, developed a theory ofself-channeling of intense electromagnetic waves in opaque supercritical plasma, and for the first time studied
the effects of self-action of relativistically strong waves associated with the dependence of the mass of anelectron on the energy of vibrations in the wave field. These effects determine the nature of the interaction ofultra-high-power laser pulses with plasma in modern experiments aimed at developing new methods foraccelerating particles and studying extreme states of matter.

In the same years, A.G. Litvak investigated a number of important effects in the field of nonlinear optics.
He predicted the effect of thermal self-focusing and constructed its theory, formulated (together with V.I.
Talanov) an equation of the type of a nonlinear Schrödinger equation to describe the self-action of threedimensional wave packets in nonlinear media, and on its basis developed the theory of modulation instability of
non-dimensional wave packets, showed the existence of nonlinear surface polaritons - electromagnetic surface
waves that have no linear analogue.
A. G. Litvak has the priority of setting up complex experimental studies of the interaction of high-power
microwave radiation with plasma. He and his colleagues were the first to experimentally discover and study theeffects of self-focusing of waves in a plasma and nonlinear transparency of dense “supercritical” plasma,modulation instability of Langmuir oscillations, and dynamics of a Langmuir caviton. Their investigations of
the nonlinear dynamics of a freely localized gas discharge in beams of electromagnetic waves laid thefoundations for a new field of low-temperature plasma physics, extremely rich in various applications: from theproduction of beams of multiply charged ions for high-energy accelerators to the purification of the upper
atmosphere from environmentally harmful impurities and ozone regeneration.
In the field of controlled thermonuclear fusion, A.G. Litvak and co-authors developed the foundations of
the theory of electron-cyclotron (EC) heating of plasma by quasi-optical beams of electromagnetic waves anddemonstrated the possibility of plasma heating in toroidal installations when radiation is input from a weakmagnetic field. These proposals, confirmed by experiments on the T-10 tokamak at the Kurchatov National
Research Center, served as the basis for the widespread use of EC heating and non-induction current generationin modern toroidal CTS installations.
A team of highly qualified theorists and experimenters was formed under the leadership of A.G. Litvak,
who achieved noticeable success in the creation of powerful sources of microwave radiation and thedevelopment of their applications in radar, plasma physics and nuclear physics, in technologies for obtaining
new materials. Among the most important results in this area should be noted the development and introduction
into production of quasi-cw gyrotrons of megawatt power level. On the initiative of A.G. Litvak, the the Closed
Joint-Stock Company "Scientific Production Enterprise 'GYCOM' (Gyrotron Complexes)" (GYCOM Ltd.) wasestablished. Its high-tech production made it possible to equip about fifteen domestic and foreign tokamaks andstellarators with efficient EC systems based on powerful gyrotrons. At present, A.G. Litvak and his colleagues
are completing the creation of a continuous megawatt gyrotron at a frequency of 170 GHz for the international
ITER project and a megawatt gyrotron with a stepwise tuning of the radiation frequency in the range from 105
to 150 GHz. Remarkable progress has been achieved in the development of sources of dense nonequilibrium
plasma based on gyrotrons of a new generation, technologies for sintering of nanoceramic materials and highspeed growth of polycrystalline diamond films and plates, and diamond single crystals.
In recent years, A.G. Litvak and his co-workers have launched research on the creation and applicationof terahertz radiation sources associated both with the advancement of traditional methods of high-power
vacuum electronics to the region of higher frequencies and with the use of detection of femtosecond laser
pulses in nonlinear media. The possibilities of realizing the basic elements of quantum communications andcomputations based on impurity centers in solids (inorganic crystals activated by rare-earth metals, vacancy
centers in diamond) are investigated. Qubits, quantum memory on the spectral lattice of rare-earth metal ionsembedded in an inorganic crystal have been implemented, a new tomography method for an optically controlled
qubit has been proposed, and the possibility of implementing three-qubit operations has been experimentallydemonstrated. A laboratory model of an atomic clock based on coherent population trapping on rubidium vapor
has been developed, demonstrating a stability at the level of 3 × 10-11 per 1000 sec.
The results of A.G. Litvak's research have been published in more than 300 scientific papers,
implemented in numerous unique instrumental and hardware complexes. His scientific achievements werenoted in the team of authors by the USSR State Prize in Science and Technology for the cycle of works"Fundamentals of nonlinear dynamics of high-frequency wave processes in fully ionized plasma" (1987), theRussian Federation Government prize in the field of science and technology "For the development anddevelopment of industrial production megawatt gyrotrons for electron-cyclotron plasma heating in large-scale
controlled thermonuclear fusion installations ”(2012), a prestigious international prize named after Kenneth
Button, Outstanding Contribution to the Science of Electromagnetic Waves (2008).
A.G. Litvak pays much attention to the education and training of young scientific personnel. Among his
students there is a corresponding member of the Russian Academy of Sciences, more than 20 doctors (DSc and
PhD). He is the founder and head of the well-known and one of the largest in Russia scientific school in thefield of plasma physics, which includes about 30 actively working researchers many of which young scientists.
A.G. Litvak is the organizer and the first dean of the basic faculty of the IAP RAS "Higher School of Generaland Applied Physics" at Nizhny Novgorod State University. He created the IAP RAS Scientific and
Educational Complex, which implements an effective continuous system of training for scientific personnel forwork in the field of physics. The complex includes specialized senior classes of physical and mathematicalsciences
A.G. Litvak is doing a lot of scientific and organizational work. He played a decisive role in theformation of the largest Branch of the IAP RAS - the Branch of Plasma Physics and High Power Electronics.
As director of the IAP, A.G. Litvak successfully solved the problems of economic, personnel and scientificsupport and development of the institute, which, despite the difficulties of recent years, has retained its leading
positions in world science in the field of physics of oscillatory and wave processes. He is doing a lot of work on
the coordination of research and the establishment of effective scientific and industrial relations of the Institutewith leading research centers and industrial enterprises of Russia.
AG Litvak is the initiator of the organization in 2008 of the Nizhny Novgorod Scientific Center of theRussian Academy of Sciences, which consolidated the intellectual and technological potential of the academic
institutions of Nizhny Novgorod. On his initiative, under the auspices of the NSC RAS in the Nizhny Novgorod
region, activities in the field of popularizing scientific knowledge were actually revived and the Scientific and
Educational Center "Knowledge - NN" was created.
A.G. Litvak is a world-renowned scientist. He is the chairman and member of the program committees
of a number of international scientific conferences and meetings, including the traditionally held IAP RAS
conferences "Frontiers of Nonlinear Physics" and "Intense Microwave Radiation: Sources and Applications",
which have a high international rating, a member of the editorial boards of a number of international anddomestic scientific journals, a member of the Council of the Russian Foundation for Basic Research. In
recognition of the merits of A.G. Litvak, he was awarded the Medal of Friendship in 2004, the Medal of Meritfor the Fatherland, IV degree in 2010, and in 2006 he was awarded the title of Honorary Citizen of the Nizhny
Novgorod Region.
In 2005, Professor Litvak was a member of the International Check and Review Committee, which
evaluated positively the research carried out at FIR UF Center during the first five years since its establishment.
As a Director of IAP-RAS, Professor Litvak has always been an active supporter of the international
collaboration between scientists from IAP and FIR UF Research Center.
The friends and colleagues of A.G. Litvak, his numerous students and followers congratulate him
on his 80th birthday and wish him good health and long life, as well as new remarkable achievements!

LIST OF SELECTED RECENT PUBLICATIONS
Bibliography and links to selected recent publications on topics related to the research field of theInternational Consortium and published after June 2020, i.e. after issuing the previous Newsletter #15.
This cumulative list is in chronological order as collected from various bibliographical and alert services
A. Publications by authors from the institutions participating in the International Consortium
Y. Yamaguchi, T. Ogura, T. Ueyama, Y. Maeda, K. Takayama, J. Sasano, M. Fukunari, Y. Tatematsu, T. Saito,"Super Multi-Frequency Oscillations at Fundamental Harmonics with a Complex Cavity Gyrotron," IEEE
Electron Device Letters, (2020). DOI:10.1109/LED.2020.3000640.
https://ieeexplore.ieee.org/document/9110568
Kojima, M., Suzuki, Y., Tasaki, T. et al., “Clinical Course of High-Frequency Millimeter-Wave (162 GHz)
Induced Ocular Injuries and Investigation of Damage Thresholds,” J Infrared, Millimeter, and Terahertz Waves(2020). DOI:10.1007/s10762-020-00714-1.
https://link.springer.com/article/10.1007/s10762-020-00714-1

G. Aiello, S. Schreck, K.A. Avramidis, T. Franke, G. Gantenbein, J. Jelonnek, A. Meier, T. Scherer, D. Strauss,
M. Thumm, M.Q. Tran, C. Wild, E. Woerner, “Towards large area CVD diamond disks for Brewster-angle
windows,” Fusion Engineering and Design, vol. 157 (2020) 111818. DOI:10.1016/j.fusengdes.2020.111818.
http://www.sciencedirect.com/science/article/pii/S0920379620303665
Girka I.O., Girka O.I., Thumm M., “Azimuthal surface waves in cylindrical metal waveguides partially filled
by magnetoactive plasma: Analysis of energy transfer,” Physics of Plasmas, vol. 27, n. 6 (2020) 062108. DOI:
10.1063/5.0009220.
https://aip.scitation.org/doi/10.1063/5.0009220
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Amplifier: Device Concept and Electron-Optical System Modeling," in IEEE Transactions on Electron Devices,(2020). DOI:10.1109/TED.2020.3001491.
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Sheet beam electron gun using axially-symmetric spherical cathodeInventors: David R. WhaleyAndrew P. Zubyk
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Microwave plasma sterilization system and applicator thereof
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Pulsed electron paramagnetic resonance spectrometer
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Compact standing-wave linear accelerator structure
Inventor: Eiji Tanabe
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