Supplementary Information Achievement of robust high-efficiency 1 MW oscillation in the hard-self-excitation region by a 170 GHz continuous-wave gyrotron KEISHI SAKAMOTO*, ATSUSHI KASUGAI, KOJI TAKAHASHI, RYUTARO

MINAMI+, NORIYUKI KOBAYASHI AND KEN KAJIWARA

Plasma Heating Technology Group, Japan Atomic Energy Agency (JAEA),

801-1Mukoyama, Naka, Ibaraki 311-0193, Japan

+Present address: Plasma Research Center, University of Tsukuba,

Tsukuba, Ibaraki 305-8577, Japan

*e-mail: sakamoto.keishi@jaea.go.jp

1. A configuration of 170 GHz Gyrotron

In Fig.S1(a), a picture of the 170 GHz gyrotron is shown. The length is 3m, and the

weight is ~800 kg. Figure S1(b) is a schematic view of the internal structure of the

gyrotron. The gyrotron is inserted in the solenoid coil of super conducting magnet

(SCM). A resonator is set at the center of the solenoid coil, where the magnetic field

is the maximum. The electron beam is emitted from the electron gun. By accelerating

the electron across the magnetic field, a rotational velocity is given. By the magnetic

mirror compression, a perpendicular-to-parallel velocity ratio α (pitch factor) of the

electron increases as the electron proceeds to the resonator. The electron gun used in

the experiment is a triode type. The triode gun has a great advantage that the pitch

factor α can be controlled independently with the acceleration voltage Vb. Here, a

mirror ratio between the resonator and the gun is Bc/Bcath~29, where Bc and Bcath are

the resonator and gun magnetic field, respectively. In the experiment, the pitch factor

is considered to be 1.2~1.6, and Larmor radius of each electron is ~0.1mm in the

resonator. A high power mm wave is excited in the resonator by the cyclotron

resonance maser (CRM) effect. The oscillated mode is converted to the Gaussian

beam by the internal launcher and four mirrors, and is transmitted quasi-optically

through the diamond window. It was experimentally identified that the 92 % of the

oscillation power is extracted from the window and the rest of the power is lost (Ploss)

as an Ohmic loss in the resonator and the launcher, and as a diffraction loss from the

launcher. The spent electron beam after the interaction has a definite minimum

energy e.g., ~25keV which is a consequence of a saturation effect related to phase

trapping of the electrons in the electromagnetic wave. By applying a retarding

potential Vd.c. between the resonator and the collector, the beam kinetic energy is

electrically recovered by the power supply, which brings about a large efficiency

enhancement ηTotal (≡ Pout

(Vb −Vd .c.)Ib

).

2. Role of each element of gyrotron

In Fig.S2, functions of each element of the gyrotron are shown. Figure S2(a) is the picture

of the electron gun. The electron emitter (a bright ring shown in the figure) makes a

hollow electron beam in the resonator. In Fig.S2(b), the field pattern of the TE31,8 mode in

the resonator is shown with the position of the electron beam. A radius of the resonator is

17.9 mm that corresponds to the cut-off radius of the TE31,8 mode at 170 GHz. The

electron beam radius is 9.13 mm to obtain the optimum coupling with TE31,8 mode. The electron beam radius rb is determined by maximizing the function Jm−1

2 (χm,nrb /rw ), where

Jm−1(χ) is the (m-1)-th Bessel function, χm,n is the n-th root of dJm (x)dx

= 0 , and rw is

the resonator radius. The thickness of the beam is thin, less than 0.5 mm, to minimize the

coupling with unwanted modes. The field distribution of the excited mode is very

complex, but this can be converted to the Gaussian beam at very high efficiency ~98 %

using a quasi-optical launcher whose inner surface has small deformation that is

numerically optimized to form a Gaussian profile at the output (ref.20,21).

Figure 2(c) is a picture of the output window. The window material is the synthesized

diamond (Chemical Vapor Deposition, CVD). The aperture is 88mm and the thickness is

1.853 mm. As a loss tangent of the diamond is one order lower than other materials and a

thermal conductivity is extremely high, 2000 W/mK, the edge water-cooling is well

capable of the power penetration of 1 MW/CW. At present, the CVD diamond is the only

window material compatible with the transmission of an RF power level in excess of 1

MW at 170 GHz.

The transition of the electron energy distribution function at the resonator is shown

schematically in Fig.S2(d). Before the CRM interaction, the electron energy is

monochromatic (72keV). After the interaction, the energy distribution has a significant

spread and shifts its mean value to lower energies. By energy conservation, the difference

in mean energies of the distributions before and after the interaction corresponds to the

oscillation power. The lowest electron energy is associated to trapping of the electrons in

the electromagnetic wave. Here, as the inherent characteristics of the CRM interaction,

the definite minimum energy exists in the spent beam, which is 25 keV in the experiment.

By applying the retarding potential on the spent beam, the electron is decelerated as

shown in the Fig.S2(d), where the energy is recovered by the power supply statically as

described in section 1.

3. Application to the fusion research

At present, the major application of the high power gyrotron is in the field of nuclear

fusion research. The gyrotron is used as a power source for an electron cyclotron

resonance heating and current drive (EC H&CD). The EC H&CD is an ideal

plasma-heating tool for fusion reactor because the RF power can be injected

quasi-optically from the launcher placed apart from the fusion plasma. Furthermore, the

resonant nature of the wave-particle interaction in the plasma makes that EC H&CD

allows to have a very local power deposition in the plasma for a control of plasma

parameters. The main issue for this type of heating, to be used in a fusion experimental

reactor such as ITER (International Thermonuclear Experimental Reactor), has been the

very difficult R&D of the gyrotron. After nearly 20 years of worldwide R&D, with this

present results, the achieved gyrotron parameters are, for the first time, fully compatible

with the ITER requirements.

In the ITER project, the EC H&CD system operating at 170 GHz with a total power of

20 MW in the plasma will be a part of the auxiliary plasma heating. The local nature of

the power deposition of the EC H&CD system allows to perform local heating as well

active control of plasma instabilities. The frequency of 170 GHz is related to the ITER

on-axis magnetic field of 5.3 T together with the fact that the obliquely injected

fundamental ordinary mode will be used for EC H&CD.

The RF pulse duration of the EC system should be longer than the plasma burning

time 400 s. The gyrotron efficiency should be as high as possible and the presently

achieved efficiency of over 55 % at 1 MW output is significantly higher than the ITER

requirement of 50 %. Previous to these results the efficiency level achieved for this type

of gyrotron was around 40 % at 170 GHz.

Figure S3 shows the configuration of the gyrotron array. For injecting 20 MW of RF

power in the plasma at 170 GHz, the EC system will be composed by 24 gyrotrons with

the associated high-voltage power supplies, RF transmission lines and real-time

controlled launchers mounted on the ITER vacuum vessel.

4. Configuration of RF transmission and absorption system.

Figure S4 shows the configuration of the gyrotron and transmission line of the output

power. The output power Pout couples with HE11 mode of the corrugated waveguide using

two phase-correlated mirrors in a matching optics unit (MOU). The RF power is

transmitted to the dummy load composed of pre- and main-dummy loads. The insides of

the MOU, the waveguide and the dummy load are evacuated to avoid the breakdown. All

components are cooled by water, therefore, the deposition powers are identified from the

temperature increase of the cooling water.

Figure captions:

Figure S1: (a) Picture of 170 GHz gyrotron. (b) Conceptual view in the gyrotron and

power supply.

Figure S2: Gyrotron elements.

(a) Picture of the electron gun.

(b) Field pattern of the TE31,8 mode in the resonator. An orange ring shows a position

of the electron beam. Radii of the resonator and the electron beam are 17.9 mm,

and 9.13 mm, respectively.

(c) Picture of the output window. The aperture is 88 mm. The window material is the

synthetic diamond. The thickness is 1.853 mm.

(d) Velocity distribution functions of the initial electron beam, after the resonator, and

after the energy recovery are shown by purple, blue and red, respectively.

Figure S3: Conceptual view of the electron cyclotron heating and current drive system

of fusion reactor.

Figure S4: Configuration of RF transmission system and dummy load.

The measured absorption powers are shown in the figure.

Main PowerSupplyVmain

Body PowerSupplyVk

AnodeVoltageController

IGBTSwitch

MainMagnet

GunMagnet

SCMDC break

MIG

e-

DiamondWindow

RF

Resonator

Electron gun (triode)

0kV

-47kV

-5kV

Vb

VDC +25kV

Figure S1

(a)(b)

Super-ConductingMagnet (SCM)

Output window

Figure S2

Electron beam

Electron Emitter

55%

At collector

(d) Distribution function of electron beam

Resonator input

Resonator output

Electron Energy

37%

72keV0keV

(b) Field pattern in theResonator (TE31,8 mode)

(c) Output window

(a) Electron gun

MainMagnet

GunMagnet

SCM

e-

DiamondWindow

Resonator

25 kVDC break

Launcher

RF beam

25keV

Fusion reactorGyrotron array

Transmission line

RF launcher

Figure S3

Figure S4

MOU

Gyrotron

Support Stand

CalorimetricLoad

Water CooledStray RF Absorber

AdjustableFocusingMirror

31.75mm Corrugated W/G

PositioningMicrometers

4-Direction AdjustablePhase Correction Mirrors

Movable Mirrorfor Calorimetric Measurement

RF Power

Dummy load

Loss in matching optics unit(MOU)0.04 MW

1m4m

2m

Transmission loss: ~0.01 MW

RF power

0.96 MWPout=1.01 MW at windowWaveguide