Proceedings of ITC/ISHW2007

Design Study on Plasma-Loaded Cyclotron Resonance Maser
Utilizing TPD-II Machine in NIFS
Kazuo MINAMI and Masaharu SUGITOa)
aTokyo Denki University, Chiyoda-Ku, Tokyo, 101-8457 Japan
National Institute for Fusion Science, 322-6 Oroshi-cho Toki 509-5292 Japan(Received 30, October 2007/ Accepted)

Design study of an experiment for plasma-loaded cyclotron resonance maser (CRM)
utilizing TPD-II Machine at NIFS, Japan is described. We derive and analyze numerically anexact linear dispersion relation of radiation from a large orbit electron beam, and found that therelation includes two principles of cyclotron emission with oscillation frequencies above andbelow the relativistic electron cyclotron frequency. The former is conventional CRM instability,
and the latter is named Cherenkov instability in the azimuthal direction (CIAD). In this study,
the existence of CIAD is tried to verify experimentally. For plasma density n > 1.5 × 1011 cm-3,
the CRM instability may be suppressed and the CIAD may take turn.
Keywords: Cavity, Cherenkov instability in azimuthal direction, cyclotron resonance maser,
fast wave, gyrotron, negative absorption, microwave, slow wave, TPD-II, wiggler.
1. Introduction
The principle of gyrotrons, high-power
millimeter microwave sources indispensable forfusion research, is believed cyclotron resonancemaser (CRM) instability [1-4]. The CRM wasverified in an experiment in which negative
 [2]. Here,absorption was observed for ω > Ωω and Ω = eB0 γ 0m are, respectively,
oscillation angular frequency and relativistic
electron cyclotron frequency.
However, all the existing linear dispersion
relations of CRM instability [3, 4] include
unphysical (numerical) modes unstable at infinite
values of axial wavenumber k z in slow wave
region, ω / k z < c , that can never be observed
experimentally. To overcome the difficulty, wederive and analyze numerically exact linear
dispersion relations of CRM for a large orbit (LO,hereafter) electron beam, for the first time in thehistory of the CRM research [5-7]. The
conventional unphysical modes are replaced bystable modes near the fast cyclotron mode. Here,LO means that all the electrons have an identicallocation of guiding center on the center axis ofwaveguide.
Our exact dispersion relations [5-7] include
two principles of cyclotron emission withoscillation frequencies above and below thebranch of relativistic fast electron cyclotron wave
 + V k . The former is well-known CRM
ω=Ωz z ) , and the latter (ω < Ω ) isinstability (ω > Ω
named Cherenkov instability in the azimuthal

direction (CIAD). The reason why the CIAD has
not been included in the existing dispersion
relations is that the boundary conditions with
inevitable finite Larmor radius effect atbeam-vacuum interface were not analyzed
correctly.
It should be emphasized, however, that theCIAD we found remains only a proposal ofpossible cause of cyclotron emission, until its
physical existence is verified experimentally. To
verify the CIAD, we try to extend the CRM
experiment in vacuum made by Hirshfield andWachtel [2] to a plasma environment.
We design and fabricate a plasma-loaded CRM
in the TPD-II Machine at National Institute for
Fusion Science (NIFS), Japan, utilizing as beamsource. With increase in density of plasma in
TPD-II, the CRM instability may be suppressed
and the CIAD may take turn. In other words,
frequency of negative absorption observed invacuum [2] may change from above to below Ωwith increase in the beam density in the cavity
such that n > 1.5 × 1011 cm-3.
2. Theoretical Study on CRM Instability andCIAD
The CRM instability [1, 2] has been believed to + V k ofbe caused by the faster branch ω > Ωz z
the fast cyclotron wave ω = Ω + V k . It must bez z

emphasized, however, that all the existing linear
dispersion relations [3, 4] of the CRM instability
include unphysical branches unstable at infinite
values of axial wavenumber kz. Gyrotron

Proceedings of ITC/ISHW2007

researchers have trusted that the growth rate neark z = 0 was still CRM instability. The fact is asfollows: Their physical explanation [3, Fig. 1] of
CRM instability was correct, but their relation [3,Eq. 1] of CRM was entirely incorrect. Both ofthem have nothing to do with each other. In orderto understand CRM instability physically, onemust take into account the logical presence ofCIAD that is unavoidable in general whenever ahigh density beam has a boundary.
We consider a circular waveguide of radius rcav
including concentric LO infinitely thin thickness
beam. If the beam is neutralized by cold ions, noradial motion of the gyrating electrons is allowed,
and they must stay on the original LO circle atany moment. The derivation of our exact
dispersion relation for infinitely thin thickness
annular beam is described in [5]. Somewhat
surprisingly, infinitely thin annular beam does notexhibit CRM instability, but CIAD is obtained.
On the other hand, when all the non-relativistic
terms in the surface current density are dropped,without legitimacy through approximation c → 0 ,to exclude the nonrelativistic effect, we obtain therelation identical to conventional linear dispersion
relations of CRM obtained by Sprangle andDrobot [3, Eq. 1], and by Chu and Hirshfield [4,Eq. 8] that include unphysical branches in thelimit of wavenumber k z → ±∞ . These classicalrelations were still understood to be correct,
because the obtained branch of CRM instability
 at kz=0 [3, Fig. 1] was qualitatively
with ω > Ω [2, Fig.
identical to the experimental fact ω > Ω2(a)]. However, this superficial coincidencecannot justify to ignore the presence ofunphysical branches in their dispersion relations.
The unphysical branches are the evidence of
inadequate derivation of the linear dispersion
relations of CRM. Such unphysical instabilities
flat for kz are observed often in numericalanalyses, but have never been observed
experimentally. A correct dispersion relation that
includes both CIAD and CRM instability is
obtained, when one analyzes a finite-thickness
LO annular beam that allows radial displacementof the electrons. Our exact dispersion relations [5,7] are exceptions that have overcome thedifficulty in a particular case of LO electron
beams for the first time in physics of gyrotrons.
3. Design Study of Plasma-Loaded CRM in
TPD-II Machine
For experimental verification of the CIAD, adesign and fabrication of plasma-loaded CRM
have been conducted. Schematic view of theTPD-II Machine and our constructed apparatus-are shown in Fig. 1. In (a), total view of theapparatus is depicted. Plasma is produced by DC
helium gas discharge between a hot cathode andgrounded anode in TPD-II at the right-side.
(a)

(b)

(c)

Fig. 1 Plasma-loaded CRM installed inside theTPD-II Machine, NIFS, Japan. (a) Total view.
(b) Principle of plasma-loaded CRM. (c)Distribution of axial magnetic field in thewiggler and the cavity. Bar code shows thelocation of 16 coils.
Plasma is emitted from a small orifice in theanode into left-side plasma container in solenoid
coils where the plasma-loaded CRM is located.
This portion is evacuated by high speed pumps toProceedings of ITC/ISHW2007

remove neutral gases for attaining fully ionizedplasma. The plasma column has high density up
to 1014 cm-3, temperature of a few eV and beam
diameter 10 mm.
To detect negative absorption caused by CRM
instability or CIAD, a large number of gyrationsof the beam inside the cavity are required. The
principle of the plasma-loaded CRM isschematically shown in Fig. 1(b). It consists
roughly of two different portions: (i) A pair ofhelical windings called wiggler in this paper for
creating transverse velocity in the beam at theright-hand side, and (ii) the TE011 mode
cylindrical cavity at the left-hand side. The latteris connected to microwave circuits for detecting
negative absorption of incident low power
microwave near 3.45 GHz. An electron beamfrom TPD-II Machine is incident from theright-hand side. The beam, however, has noazimuthal velocity component, namely Vθ  0 .
In order to create a large Vθ for gyrations, thebeam is introduced on the axis of the wiggler that
produces a helical circularly polarized static
magnetic field bt of the order of 10−3 (T) near
the axis. Here, bt can be quite small, because it
does not give any energy to the beam. In Fig. 1(c),calculated distribution of axial magnetic field on
the axis of the plasma-loaded CRM is shown.
If the pitch length λw of the right-handcircularly polarized DC magnetic field

bt

generated by the wiggler is equal to axial pitch , the electrons are accelerated inlength 2π Vz / Ωazimuthal direction secularly by the Lorentz force
G G− ev z × bt at the expense of their axial velocity.
The designed wiggler is a pair of four turn bifilar
conductors with pitch length λw = 8.0 cm,
radius a = 1.775 cm and total length L = 32cm. The pitch factor α = Vθ / Vz  0.65 will beobtained at the exit of the wiggler.
The obtained α can be increased further, bytransmitting the beam before the incidence on thecavity through the mirror field shown in Fig. 1(c)from Bs=0.03268 T at the wiggler to another axial
field B0=0.1268 T at the cylindrical cavity. Themirror ratio is B0/Bs=3.88, and α =1.28 will beobtained that enables many gyrations in thecavity.
In Fig. 2, expected electron properties throughwiggler and mirror magnetic field aredemonstrated by trajectory tracking in order toshow an example that helical field bt enhances
perpendicular pitch α = Vθ / Vz . In (a) and (b), theprofiles of axial and perpendicular magnetic
fields, Bz, Br and Bθ on the axis, are calculated.
In (b), Br and Bθ with and without bt=0.0008 T(Itot=40 A) are depicted. In (c), an example ofradial position of electron trajectories is followedfrom z=-1.1 to 0.3 m for both cases bt=0.0008 T
and bt=0. In (d), changes in perpendicular pitch
α = Vθ / Vz are depicted for both bt. It is clearlyshown in (c) and (d) that the presence of wiggler
magnetic field bt=0.0008 T enhances significantly
the spiral motion.
The frequency of incident microwave on thefabricated cylindrical stainless-steel cavity works
at TE011 mode near 3.5 GHz. Inner diameter ofthe TE011 cavity is 0.1083 m, and the length isvaried from 0.17 to 0.21 m by the adjustable
shorting disk. Figure 3 shows the calculated
curves of positive and negative absorptions as afunction of axial magnetic field B0. The frequencyof incident microwave is adjusted at theresonance in empty cavity to observe theminimum | Rmax |2 . The vertical axis | R |2 isassumed to be proportional to attenuation
constant α for round-trip of microwave in thecavity as [1, 2]:πG ⎛2 py ⎞
ω − ω1 ,α=1+,y=Qe ⎜⎝ 1 + y 2 ⎟⎠2 B1

ω1 , B1 and p are given numericalconstants to fit the positive and negativeabsorptions. In Fig. 3, coupling factor s=0.15 andother parameters shown in the figure are assumed.
Negative absorption (in fact, decreased positiveabsorption) arises for | p |> 1 [1]. The resonant
curve of the CRM instability for p=1.5 is depictedby solid curve, whereas the case of the CIAD for
p=-1.5 is shown by dashed curve. Negative
absorption of the CRM instability and the CIAD
 andcould be observed, respectively, for ω > Ωω < Ω as shown in Fig. 3. In other words, theCRM and the CIAD are expected for low-field that corresponds
and high-field sides of ω = Ω
to the axial magnetic field B0 = 0.3106 T for ourwhere15 keV beam.
According as beam current increases, theregion of the negative absorption is expected tomove from left-hand side (solid curve) toright-hand side (dashed curve) of B0 = 0.1306 T.
Or, probably we may observe both negative
absorptions at the same time for the incidence ofhigh density beam such as n > 1.5 × 1011 cm-3,
where n = 1.5 × 1011 cm-3 corresponds to =ω .
ω=Ωb

Proceedings of ITC/ISHW2007

Eb=15 keV, α(initial)=0.001,λw=8 cm

0.15Bz (T)(a) AXIAL MAGNETIC FIELD

0.1

CavityWiggler

Br, Bθ (T)

0.05
00.0020.001
0-0.001-0.002Br (r=0.005 m)

0.015(c) RADIAL POSITIONr (m)measurements of negative absorption caused by
the CRM instability and the CIAD will beconducted.

(b) PERPENDICULAR MAGNETIC FIELDS
Br (r=0.01 m)

Bθ
bt=0.0008 T

Fig. 4 Constructed microwave interferometercircuits including fabricated TE011 mode
cylindrical two-port cavity with resonant
frequency near 3.45 GHz.

0.010.005

bt=001.5
α=Vθ/Vz(d) PERPENDICULAR PITCH

1bt=0.0008 T

0.50bt=00-0.5-1

AXIAL POSITION z (m)Fig. 2 Electron beam properties obtained bytrajectory tracking. Helical field bt enhances
significantly perpendicular pitch α = Vθ / Vz .

REFLECTED POWER |R| 2

Eb=15 keV, Q0=500, Qe=3300, ω/2π=3.55 GHz
p=1.53Positive Absorption
by Cold Electrons
at 0.1268 T2(CRM)
p= -1.5(CIAD)
p=01
Negative Absorptions near 0.1306 T

00.126

0.128

0.13

0.132

AXIAL MAGNETIC FIELD B 0 (T)Fig. 3 Curves of absorption expected for CRM(solid curve) and CIAD (dashed curve).
The physical meaning of | p |> 1.0 for
negative absorption is physically analogous toN (Vθ / c ) 2 > 1 that many gyrations in the cavity
are required for detecting the resonant curves
correctly, where N  1 is number of gyrations inthe cavity.
Diagramofconstructed
microwave
interferometer including the TE011 plasma cavity
is shown in Fig. 4. In near future, the4. Discussion and Conclusion
Currently, it may not be a fashionable subjectof research to discuss which oscillation frequency
 or ω < Ω
 is observed in real gyrotrons.
ω>Ω
This is partly because ω is almost a fixed
quantity given by the sizes of a cavity. Moreover, is and ω < Ω
the distinction between ω > Ωpractically difficult from experimental point of
 is a quantity spatiallyview, because Ω
non-uniform, whereas ω can be measured very
precisely. The difference between ω and Ω
can be observed, only when a device to fit theparticular purpose of distinction between CRM
and CIAD were carefully designed [2].
The CIAD and the CRM instability areprobably coexisting mechanisms of cyclotron
emission from various gyro-devices incliding the ) may not
gyrotrons. The CRM instability ( ω > Ω
be the exclusive principle of gyrotron oscillation,because there has been no experimental
 in gyrotrons. It is quite
verification to be ω > Ω andimportant to distinguish between ω > Ω
incyclotron
emissionsinplasmaphysics
ω<Ωand in gyrotron research, since physical reasonsare different. It should be emphasized that,sometimes, physics requires a stringent accuracy
for better understandings, even though suchaccuracy may not be required from engineering
point of view.
The gyrotron community over the world ispartly spoiled by the defect of unphysicalsolutions [3,4]. We regret that fundamental
understandings of physics of gyrotrons are notvery firm yet, although there exist huge amountof research reports for technical and hardware
developments. For decades, many of students inuniversities over the world are left to study theincorrect theory of CRM.
Our constrained gyration model and theresultant CIAD [5] remains only a proposal at thisProceedings of ITC/ISHW2007

moment, until the physical existence is verified
experimentally. It is the purpose of ourexperimental program to verify a physical causeof cyclotron emission that has not been known upto date. In our plasma-loaded CRM, negative
absorption due to the CRM instability may besuppressed in high-density beam such as 2 , namely density n > 1.5 × 1011 cm-3,
ωb2  Ωand the CIAD may take turn. In this experimental
program, we try to observe the new principle ofcyclotron emission different from the CRM
instability. The present experimental study
contributes to a deeper understanding and awidened future prospect in gyrotron research.
This work is carried out in a collaborative
research program NIFS04KQHH002, under thesupervision of Professor Kuninori Sato, NIFS,Japan.
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