Proceedings of ITC/ISHW2007

Direct Measurement of an Electron Bernstein Wave on the Internal
Coil Device Mini-RT
E. Yatsuka, D. Sakata, K. Kinjo, J. Morikawaa), Y. Ogawaa)
Graduate School of Frontier Sciences, Univ. Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa-shi, Chiba 277-8561, Japana)High Temperature Plasma Center, Univ. Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa-shi, Chiba 277-8568, Japan(Received 15 October 2007)

Measurements of electron cyclotron range of frequencies (ECRF) electric fields by using small (5 mm) antenna
have been carried out in the Mini-RT device, and signals having two characteristics of electron Bernstein wave
(EBW) have been detected. One of them is short wavelength (~2 cm). The order of corresponding refractive index
is 10, while calculation predicts several 10 to 100. The other characteristic is backward wave, i.e. group velocity isopposite to phase velocity. In the Mini-RT device, plasma production is achieved by using ECH, therefore we canexpect the existence of high-energy electrons. High-energy electrons can affect dispersion relation, and waves
having relatively long wavelength can propagate around upper hybrid resonance (UHR).
Keywords: electron Bernstein wave, mode conversion, electrostatic mode, backward wave, overdense plasma,density gradient, cyclotron harmonic resonance, upper hybrid resonance, interferometry, antenna

Electron Bernstein Wave (EBW) is one of the mostpromising methods for high beta plasma heating. This
wave can propagate across magnetic surfaces without
density limit and strongly be damped due to cyclotron
harmonic damping. However, EBW is an electrostatic
mode and its wavelength is comparable to electron Lamor
radius [1], thus it is hard to launch EBW directly into
plasma except for the special case as slender plasma, e.g.
glow discharge positive column plasma [2]. In Ref. [2],the first observation of EBW radiation, i.e. inverse
process of absorption, was discussed.
Excitation of EBW in plasma via mode conversion
process [3] is needed to achieve EBW heating for thickplasma, e.g. fusion plasma. In linear device, electron
cyclotron range of frequency (ECRF) electric field inplasma was investigated by using wire antenna [4]. As aresult, mode-converted EBW was observed with so-called
fast X-B method. Recently, mode conversion efficiencies
have been evaluated by using electron cyclotron emission(ECE) via mode conversion from EBW toelectromagnetic waves [5,6]. This method is suitable forstudying EBW heating without disturbance, but it ishardly applicable for devices that have steep magnetic
field gradient such as internal coil device.
Internal coil devices have been constructed toinvestigate high beta plasma confinement [7,8], which isbased on the theory of self-organized states in flowing
plasma [9]. The objective of this research is production ofhighly overdense plasma by using EBW heating.
author’s e-mail: yatsuka@ppl.k.u-tokyo.ac.jp

This Letter reports the preliminary results of ECRF
electric field measurements in the internal coil device
Mini-RT (Miniature Ring Trap). We produce plasma by
injecting an X-mode microwave (2.45 GHz, 2.5 kW c.w.).
High Temperature Superconductiong (HTS) Coil, that iscalled Floating Coil (F-Coil), produces poloidal magnetic
field, which is similar to that of a planet. Typical strengthof magnetic field is 0.01-0.1 T. Figure 1 shows twomagnetic configurations in Mini-RT, i.e. (a) Dipoleconfiguration and (b) Separatrix configuration. Solid(Dotted) lines denote magnetic surfaces (magnetic fieldstrengths). Figure 2 shows typical radial profiles ofelectron density; (i) Dipole configuration, (ii) Separatrix
configuration. By applying Levitation Coil (L-Coil)

Fig.1

Cross section of the Mini-RT device. (a)Dipole configuration (L-Coil current is notapplied) (b) Separatrix configuration

Proceedings of ITC/ISHW2007

Fig.2

Radial profiles of electron density ne. (i)Dipoleconfiguration,(ii)Separatrix
configuration.

Fig.4

Fig.3

Perpendicular refractive index of hot wave
with typical density profile of Mini-RT.

current, we can produce separatrix, and plasma is
confined in closed flux surfaces. We can also create steep
density gradient region (Ln ~ 5 cm) around separatrix[10,11]. Peak density is around cut-off density of
2.45GHz, O-Mode microwave, i.e. 7.6 × 1016 m-3.
Dispersion relation predicts that typical value of
perpendicular refractive index of EBW is several 10 to100. Figure 3 shows calculated radial profile of refractiveindex on mid-plane for 1.0 GHz. We assumed trapezoidal
density profile, which is similar to Fig. 2 (ii); and electron
temperature is uniformly 10 eV, which is typical value ofLangmuir probe measurements [11]. We calculated
dispersion relation of hot wave [12] propagating

Top view of Mini-RT and block diagram ofcircuit.

perpendicular to magnetic field. We assumed
perpendicular injection of X-Mode from low field side,which is one of the most appropriate for mode conversion
to EBW. Injected X-Mode electromagnetic wave tunnels
evanescent region which lies between right hand cut-off(R-Cutoff) and upper hybrid resonance (UHR), i.e. 310 <R < 315 mm. Energy of X-wave transfers into EBWaround UHR.
Mode conversion efficiency C have been evaluatedbyC = 4e −πη (1 − e −πη ) cos 2 (φ / 2 + θ ),(1a)
1/ 2
1 + α 2 −1αΩLη= e n ,222cα + 2 Ln / LB  α + ( Ln / LB ) 1 + α (1b)

α=

ω pe

Ω e UHR

where c, Ω e ,,ω pe , Ln and LB(1c)are light speed,

electron cyclotron frequency, electron plasma frequency,

Proceedings of ITC/ISHW2007

Fig.5

Interferometer traces for φ ph = ±π / 2 , 0.
Frequency of a launched wave was 1.0 GHz. We
can obtain fluctuated data, and signals areaveraged over each millimeter to determine
amplitude and phase of an ECRF electric field.

characteristic length of density and that of magnetic field,
respectively [13,14]; and φ is the phase difference
between X-Mode propagating toward L-Cutoff andreflected component propagating toward the UHR; and θis the phase of Γ(iη / 2) . By using expression (1a)without considering phase effect, i.e. term of cosine is unity,
we obtain 70~90 % mode conversion efficiency withseparatrix configuration in Mini-RT.
To investigate mode conversion process in plasma
directly, we launch X-Mode microwave by using
ceramic-coated dipole antenna (element length is 100 mm).
Frequency and power of diagnostic microwave are 1-2.1GHz, 10 W, respectively. By using lower frequencies thanplasma heating, i.e. 2.45 GHz, we can investigate waves inoverdense plasma even where underdense region ofheating microwave. To avoid penetration of high power ofmicrowave with 2.45GHz, we set band pass filter (BPF,-44.5 dB @2.45 GHz). Figure 4 shows the block diagramof ECRF electric field measurements. We can obtain DC
voltage signalrrr
E 0 (r ) + E1 (r ) cos[φ (r ) + φ ph ],rrr(2)

where E0 (r ) , E1 ( r ) , φ (r ) represent offset, amplitudeof ECRF electric field and phase of that, respectively. We
can control an external phase shift φ ph to determine therrrparameters E0 (r ) , E1 ( r ) and φ (r ) . Spatial profilesof ECRF electric fields are detected by using coax-fed
monopole (element length is 5mm, direction is toroidal)
antenna movable radially.

Fig.6

Radial profiles of phase of ECRF electric fieldwith (a) 1.0 GHz, (b) 1.2 GHz, (c) 1.5GHz

Figure 5 shows toroidal component of an ECRF
electric field on the mid-plane with separatrix
configuration. We can see a characteristic of shortwavelength related with the EBW around major radius
R=300 mm in Fig. 5. Roughly evaluated wavelength ofthat is 2 cm, while 30cm in vacuum. Therefore the orderof refractive index of EBW is 10. Location of the Last
Closed Field Surface (LCFS) was major radius R~300mm.
The EBW was detected at steep density gradient region.
Radial profiles of phase of ECRF electric field withseveral frequencies are shown in Fig. 6. We used data forthree external phase shifts that were averaged over eachmillimeter. The characteristic of phase reversal has been
seen for each frequency. Dotted lines in Fig. 6 denote thelocation of cyclotron harmonic resonance layers on
mid-plane. Phase reversal phenomena occur between 3rd
and 4th harmonic ECR for 1.0 and 1.2 GHz, 4th and 5th
harmonic ECR for 1.5 GHz. And the location of it
coincides with short wavelength region.
We can consider the direction of group velocity, i.e.
energy flux, is inward of the device. While positive(negative) gradient of relative phase with respect to major
radius means phase velocity is outward (inward) of thedevice. Thus phase reversal region suggests the directionof phase velocity v ph is opposite to group velocity v g .
From the dispersion relation, we can find that the EBW
has the characteristic of backward wave, i.e. groupvelocity v g is negative [15]. Therefore Fig. 6 alsosuggests the direct detection of EBWs between cyclotron
harmonic resonance surfaces, e.g. 3rd and 4th ECR for 1.0
GHz injection.
As well known, ECH enables to produce high- energy

Proceedings of ITC/ISHW2007

Fig.7

Radial profile of perpendicular refractive
indices, for 1 GHz, of hot waves with (a) allelectrons has temperature of 10 eV, (b ,c ,d)10%, 30%, 100% high-energy electrons hasthat of 5 keV. Dotted lines denote the locationof harmonic ECR on mid-plane.

electrons due to quasi-linear diffusion of resonant electrons[16]. In the Mini-RT device, plasma is produced by ECH,
thus we have prospects of production of high-energy
electrons. We estimate effective temperature ofhigh-energy electron is 5 keV by using scaling law of Ref.
[17].

ρ / L = 5 − 6 × 10 −2 ,(3)where ρ and L are high-energy electron Lamor radiusand magnetic scale length, respectively. We have estimatedL ~ 4 cm and B = 0.0875 T.
We have assumed electron distribution function is twocomponents isotropic Maxwellian, i.e. summation of bulk
electrons (10 eV) and high-energy electrons (5 keV), forsimplicity. We have calculated for four cases, i.e. (a) nohigh-energy electrons, (b) 10% of them exist, (c) 30% ofthem exist and (d) hot electrons. We have also assumed
F-Coil current IF is 30 kA and L-Coil current IL is 15 kA,
which are equal conditions for Figs. 5 and 6. In thisconfiguration, mode conversion occurs between 3rd and4th harmonics of ECR. Dispersion relation of hot waves
propagating perpendicular to magnetic field is written as

ε xx (ε yy − n 2 ) − ε xy ε yx = 0,(4)

where n and ε are refractive index and specific dielectric
tensor of hot waves [12], respectively.

High-energy electrons affect dispersion relation of hotwave especially around the UHR. If there is nohigh-energy electron, i.e. in the case of (a), refractive index
dramatically rises around UHR. Refractive indices haverelatively long wavelength region (refractive index issmall) with increasing of high-energy electrons. The reason
why refractive indices, for (b) and (c), are so complex isdue to assumption of two components Maxwellian
distribution function. Finite Lamor radius (FLR) effectfrom high-energy electrons around UHR enables
propagation with long wavelength.
On the other hand, refractive indices show identicalcharacteristics around 3rd harmonic ECR, for the case with(a), (b) and (c) of Fig. 7. Around resonance region,
wavelength is comparable to Lamor radius, therefore
sufficient FLR effect from bulk electrons can be expected.
In summary, ECRF electric field measurements byusing antenna have been carried out in the Mini-RT device.
And signals having two characteristics of EBW, i.e. shortwavelength (~ 2 cm) and backward wave, have beendetected. Dispersion relation predicts that typical value ofrefractive index of EBW in Mini-RT is several 10 to 100.
However roughly evaluated refractive index is 10experimentally. Plasma production in Mini-RT is achievedby ECH, therefore we can expect the existence ofhigh-energy electrons. We evaluated the effects ofhigh-energy electrons to dispersion relation, and obtained
relatively long wavelength region around UHR.
The authors would like to acknowledge Dr. T.
Kaneko for his technical advices for measurements. Theauthors also thank to Prof. T. Mito and Dr. N. Yanagi for
discussion about cooling superconducting magnet andexcitation of it.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]

I. B. Bernstein, Phys. Rev. 109, 10 (1958).
K. Mitani and H. Kubo, J. Phys. Soc. Jpn. 19, 211 (1964).
T. H. Stix, Phys. Rev. Lett. 23, 878 (1965).
H. Sugai, Phys. Rev. Lett. 47, 1899 (1981).
G. Taylor et al., Phys. Plasmas 9, 167 (2002).
B. Jones et al., Phys. Rev. Lett. 90, 165001 (2003).
Y. Ogawa et al., J. Plasma Fusion Res. 79, 643 (2003).
Z. Yoshida et al., Plasma Fusion Res. 1, 008 (2006).
S. M. Mahajan and Z. Yoshida, Phys. Rev. Lett. 81, 4863
(1998).
[10] T. Goto et al., Jpn. J. Apl. Phys. 45, 5197 (2006).
[11] E. Yatsuka et al., Trans. Fusion Sci. Tech. 51, 310 (2007).
[12] T. H. Stix, Waves in Plasmas (American Institute ofPhysics, 1992) p. 257-262.
[13] A. K. Ram and S. D. Schultz, Phys. Plasmas 7, 4084
(2000).
[14] A. K. Ram et al., Phys. Plasmas 3, 1976 (1996).
[15] F. W. Crawford et al., J. Geophys. Res. 72, 57 (1967).
[16] C. F. Kennel and F. Engelmann, Phys. Fluids 9, 2377
(1966).
[17] N. A. Uckan, Phys. Fluids 25, 2381 (1982).