Electron cyclotron resonance heating experiments in the GAMMA 10 tandem mirror

E L S E V I E R Fusion Engineering and Design 26 (1995) 241 250

Fusion Engineering and Design

T.

Electron cyclotron resonance heating experiments in the G A M M A 10 tandem mirror

Sai to , Y. K i w a m o t o , Y. T a t e m a t s u , Y. Y o s h i m u r a , T. T a k a h a s h i , A. K a s u g a i ~, F. K i r a 2, I. K a t a n u m a , N. Y a m a g u c h i , T. T a m a n o

Plasma Research Center, University of Tsukuba, Tsukuba City, lbaraki 305, Japan

Abstract

Two aspects of ECRH experiments in the GAMMA 10 tandem mirror are described. One is hot electron production in a minimum-B anchor cell by second harmonic ECRH. When a resonance region is located at the centre of the anchor cell, hot electrons are piled up near the centre region and the //-value attains more than 20%. For off-centre resonance, hot electrons have a spatial profile like a baseball seam. This profile is explained by a drift orbit of an electron in a minimum-B field. The other topic is observation of an intense axial electron flow with energy from hundreds of eV to a few keV generated by fundamental ECRH in the end cells. The force due to the fundamental ECRH driving heated electrons into the mirror loss cone is particularly strong. A bounce averaged Fokker-Planck code with a quasi-linear diffusion operator reproduces the electron flow with the same energies. The electron flow is a predominant ingredient for generation of the electrostatic potential in the GAMMA 10.

1. Introduction

According to the original scenario of a tandem mirror, electron cyclotron resonance heating (ECRH) is assigned two basic missions [1,2]. One is the production of mirror-confined hot electrons for enhancement of the thermal barrier depth (at position b in Fig. 1) and the other is electron heating at the plug region to raise the ion confining potential (at position p). Production of thermal barrier hot electrons by second harmonic

Permanent address: Naka Fusion Research Establishment, JAERI, 801-1 Mukoyama, Naka-machi, Ibaraki 311-01, Japan.

2 Permanent address: Nippon Telephone and Telegram Co., 1-2356 Take, Yokusuka City, Kanagawa 238-03, Japan.

E C R H has been reported [3,4]. In this paper, the effect o f the fundamenta l E C R H at the plug (plug E C R H ) is described. In particular, observat ion o f an intense axial flow o f warm electrons generated by the plug E C R H is presented. The actual process o f potential format ion is different f rom the original scenario in the G A M M A 10 tandem mirror and the electron flow has an impor tant role in potential format ion [5-10] .

End-loss electrons driven by E C R H in a mirror field have been studied in a few papers [ 11,12] and generation mechanisms have been discussed f rom the viewpoint o f quasi-linear diffusion. In the present experiment, microwave power was injected in a collimated beam and locally absorbed. By making use o f this geometry, we have iden-

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242 T. Saito et al. / Fusion Engineering and Design 26 (1995) 241 250

Cell Cell Cell

1 I ] ndiate 0 . . . . . . . . . t . i i i i i i i i I i f " ~ - . ~ . . . . i

5 10 15 z(m)

Fig. 1. Axial profile of the magnetic field of GAMMA 10. Here, only one half is plotted and the profile is symmetrical with respect to the origin of the z-axis. The positions a, b and p denote the heating regions of the anchor ECRH, barrier ECRH and plug ECRH, respectively.

tiffed diffusion of electrons along heating characteristics in velocity space [13]. Moreover, the gradient along a field line at the plug position as shown in Fig. 1 leads to the generation of a particularly intense electron flux [14]. In this paper, we examine characteristic features of the plug-ECRH generated electron flow.

In addition to the basic roles, the production of hot electrons with a high fl value in a minimum-B anchor cell has a new mission of ECRH (anchor ECRH at position a) for M H D stabilization. Hot electron production in a minimum-B field has a long history [15]. However, there has been no report on a spatial profile of produced hot electrons with a feature particular to a minimum-B field. Recently, a spatial profile like a baseball seam obtained from the Constance-B experiment has been reported and this profile has been discussed from the viewpoint of the drift orbit of an electron in a minimum-B field [16]. In G A M M A 10 the microwave power is injected in a well collimated beam also in the anchor cell. This allows us to examine the relationship of the spatial profile of the hot electrons to the location of the resonance surface and a baseball seam-like profile is also observed in our experiment. On the other hand, when the second harmonic resonance is located at the centre of the anchor cell, hot electrons are piled up near the centre region and we have produced hot electrons with a fl value of more than 20% in this case.

The experimental set-up is given in Section 2, the production of hot electrons in the anchor cell is described in Section 3, observation of the electron flow and diffusion of electrons in velocity space are discussed in Section 4 and Section 5 summarizes this work.

2. Experimental

2.1. G A M M A 10 device

The G A M M A I0 device has a carefully tailored magnetic field configuration as illustrated in Fig. 1 [17]. Two M H D anchors of minimum-B geometry are connected to both sides of the central solenoid. At both ends of the anchor cell end mirror cells are placed. The end cell has an axisymmetric configuration. The mirror ratios of the central cell, the anchor cell and the end cell are 5, 3 and 6, respectively. For a standard plasma shot the field strengths at the mid-plane of each cell are 0.405, 0.610 and 0.497 T. Ion cyclotron heating is carried out in the central cell. Neutral beams are injected into the end cells for formation of a sloshing ion distribution. Plasma shots are usually initiated by firing plasma guns located on both end walls.

Fig. 2 shows the end mirror cell and the end region that extends from the outer mirror throat of the end cell to electrically floating end plates. The magnetic field strength at the mirror throat is 3.0 T and decreases to 0.01 T at the end plate. The role of the plates is control of the radial potential profile and reduction of the non-ambipolar radial transport [ 18]. Each piece of the plates is connected to the machine ground with a high resistance.

2.2. E C R H system

A 28 GHz gyrotron for ECRH in the end cell delivers a maximum power of 200 kW in the TEo2 mode. Four gyrotrons are used in both ends (two per each cell). The microwave power is radiated from a Vlasov antenna installed in the vacuum vessel which converts the TE02 mode into the linearly polarized extraordinary mode. The beam is collimated within F W H M ~ 11 ° in the H-plane and F W H M ~ 7 ° in the E-plane. It is launched upwards at an angle of 50 ° to the z-axis as shown

to t h e c e n t e r

T. Saito et al. / Fusion Engineering and Design 26 (1995) 241-250

I1 B=I.0T

243

z-axis

28GHZvlasov - - .~ Endplates [ ~ LED

e~ J.

I I I I 0 1 2 3 m

Fig. 2. Cross-section of the end mirror cell and the end region. Microwave power is injected on to the 0.5 T resonance surface (barrier ECRH) and the 1.0 T surface (plug ECRH) from the Vlasov antennas. The LED is installed behind the innermost end plate.

in Fig. 2. The barrier ECRH power is injected on to the second harmonic resonance surface (B = 0.5 T) located near the mid-plane of the end cell. The plug ECRH power is launched from the high-field side of the resonance surface (B = 1.0 T) to avoid right-hand cut-off. Strong absorption is expected at the magnetic beach [5].

A 41 GHz, 200 kW gyrotron in the TE02 mode is used in the anchor cell. A Vlasov-type antenna radiates a collimated microwave beam with F W H M ~ 8 ° in the H-plane and F W H M ~ 5.5 ° in the E-plane in the extraordinary mode as shown in Fig. 3. The mode-B surface of the second harmonic resonance (B = 0.73 T) forms a closed surface in a minimum-B field and the distance from the centre of the anchor cell depends on the coil current.

2.3. Diagnostics

The flux and the energy spectrum of the end- loss electrons are measured by a multi-grid energy

analyzer (loss electron diagnostics, LED) [6]. The LED is installed behind the end plate and it measures the end-loss electrons through a small hole on the plate (see Fig. 2). A sawtooth voltage is applied to the electron repeller grid and the energy spectrum of the end-loss electrons can be measured in one shot. The maximum electron repeller voltage is 20 kV. The magnetic field line that passes through the LED corresponds to the radial position of 2.8 cm in the plug and 4 cm in the central cell. A silicon surface barrier (SSB) detector placed on the end wall is used to examine the energy spectrum of end-loss electrons with energies higher than 10 keV [19].

The spatial profile of X-rays emitted from the hot electrons in the anchor cell is measured by a set of two pinhole cameras [20]. A two-dimen- sional image of the X-rays is focused on a micro- channel plate (MCP). A pulse voltage is applied to the MCP and an X-ray image of a specified time interval is obtained. The angle between the line of sights of the two cameras is at about

244 T. Saito et al. / Fusion Engineering and Design 26 (1995) 241 250

Antenna 1 Antenna 2A

I ir j

Magnetic Field Line

z-axis

/ Resonance Surface (Bo=0.73T) Resonance Surface (Bo=0.64T)

Resonance

I I l m

Fig. 3. Cross-section of the anchor cell. Both of the two antennas are used for second harmonic heating. Mode-B surfaces corresponding to different magnetic field strengths at the centre of the anchor cell are illustrated.

right-angles and hence we can extract informat ion on the spatial profile o f the hot electrons f rom the X-ray images simultaneously taken by the two cameras.

3. Hot electron production in anchor cell

We have examined the spatial profile o f hot electrons produced in a min imum-B anchor cell. In Fig. 4 are shown two typical examples o f the X-ray image taken by a pinhole camera. The microwave power is launched f rom antenna 1 in both cases. Fig. 4(a) represents an image for the

center resonance case in which the second harmonic resonance region is located at the centre o f the anchor cell ( the vacuum magnetic field strength B 0 at the centre o f the anchor cell is 0.73 T; see Fig. 3). The observed image shows that the hot electrons are piled up near the centre region of the anchor cell in this case.

When the magnetic field strength is lowered, the resonance surface forms a closed shell as illustrated in Fig. 3. Fig. 4(b) shows an X-ray image of this case (B0 = 0.64 T). The image is bounded within a C-shaped area. This is considered as the projection o f the drift orbits o f the hot electrons. Electron heating occurs on the intersection region

T. Saito et al, / Fusion Engineering and Design 26 (1995) 241-250 245

(a)

I (b) I

_ z - _ ~ y ±

10 cm i Midplane

Fig. 4. X-ray images for (a) centre resonance and (b) off-centre resonance taken by a side-view pinhole camera. These images are mapped back to the same cross-section as that of Fig. 3.

of the microwave beam and the resonance surface. The magnetic field strength in this region is a minimum along a magnetic field line and electrons are perpendicularly heated. Therefore, their pitch angle is almost 90 ° and they drift on the resonance surface on which the magnetic field strength has the same value as that at the heating point. In a minimum-B field the drift orbit forms a closed curve like a baseball seam. The observed X-ray image supports this idea. For off-centre resonance heating with another antenna 2A as shown in Fig. 3, the spatial profile is different from Fig. 4(b). This is because electrons are heated in a region where the magnetic field strength is not minimum

. . . . i . . . . i ' ' • i . . . . '

A 10 ms | 1

[ ] 3S m s

0 5s ms 0 0

6

• ~ 4 0

g e~ 2

0 i •

0.4 0.5 0.6 0.7 0.8 B0(T)

Fig. 5. Diamagnetic signal plotted as a function of the vacuum magnetic field B o of the centre of the anchor cell. The different symbols represent different pulse widths of ECRH power ( A, 10 ms; E], 35 ms; O, 55 ms). The lines are guides to the eye.

along a field line and hence electrons bounce a long distance.

The stored energy of the hot electrons depends on B0. It is represented by the diamagnetic signal

taken by a diamagnetic loop located near the mid-plane of the anchor cell. Fig. 5 shows plots of

as a function of B0. The maximum value of is obtained for centre resonance (B0~ 0.73 T). The different symbols in Fig. 5 represent various pulse widths of the heating power. For a longer pulse width • attains a maximum at a slightly larger B 0. There are two possible reasons. One is the finite /~ effect. The magnetic field strength becomes smaller than B0 owing to the finite/L The increment of the optimum Bo is consistent with the reduction of the magnetic field estimated from the/~ value for each pulse width. The other possible reason is the relativistic effect. Pulse-height analysis of emitted X-rays using an NaI scintilla- tor evaluates the temperature of the hot electrons higher than 100 keV at 10-20 ms after turning on ECRH and B 0 should be larger to cancel the shift of the cyclotron frequency due to the relativistic effect.

For estimation of the stored energy from the diamagnetic signal it is necessary to take account of the finiteness of the spatial profile. We can estimate the/~ value for the spatial profile of the

246 T. Saito et al. / Fusion Engineering and Design 26 (1995) 241-250

centre resonance case by using the correction factor calculated in [21]. The estimated maximum/? value attained is 20% at the mid-plane.

4. Electron flow generated by the plug ECRH

4.1. O b s e r v a t i o n o f e l e c t r o n f l o w

Plasmas are sustained by a combination of the barrier ECRH, ICRF in the central cell. The plug ECRH is turned on after a quasi-steady state is attained. Fig. 6 shows typical wave forms of representative plasma parameters. Application of the plug ECRH leads to an instant increase in the central cell potential q~c, while the end plate potential ~EP decreases substantially from the machine ground. The plug ECRH simultaneously induces an intense flux of end-loss electrons, as

s h o t ~ o . = 1 4 4 8 3

(") .... '21

-5 .0~ xdu 1~0

' ° ° " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1000 0 BPCC00

° ' ° d ~ l~u 1~0

0.4: ....................... :j: :i0

Time (ms)

Fig. 6. Wave forms of representative p lasma parameters: (a) the plug E C R H pulse; (b) the central cell line density in cm-2; (c) the plasma potential at the central cell in volts; (d) the end plate potential in volts; (e) the end-loss electron current measured by the LED. The pulse train corresponds to the saw- too th voltage applied to the electron repeller grid.

1.2 . . . . I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' '

1

0 .8

0 .6

0.4

0.2

0

0 I I , I i , i I i i , l l i i l l i i 1 1 i i I , , , I , I Q I i i

-8 -4 0 4 8 x at plug position (cm)

Fig. 7. Radial profile of the end-loss electron current measured with a multi-grid analyzer in front of the end plates. The x-axis is in the vertical direction of Fig. 2.

shown in the bottom trace of Fig. 6. In Fig. 7 the observed profile of the end-loss electrons is plotted along the vertical direction. A multi-grid energy analyzer in front of the end plate is used in the measurement and the electron repeller voltage is fixed at the machine ground. The observed profile coincides with the vertical profile of the heating power on the 1.0 T surface [5].

Fig. 8 shows energy spectra of the end-loss electrons measured by the LED. The flux I e flow-

10 4 . , • , , ~ . , ~ , , , , , , ,

# 1 1 2 9 3 6 ~ ! 1 2 9 3 7 90ms PG on

103 "-:'%.'.. 150 kW

'. ":.'::- .......... d

""-'..2.'.'ii" :Z::: 2 ...................... 102 .2: 2?" kw

101 :. ........... ::...::: ................. IZI!! • .o . "" . . . . . . . . . . . . . . . . . . . .

• ~ "'-. 50 kW " ............ .. 222222 ............... ".. " . . . . . " . . , . . . . . . . " " " • ' , . . . . . . . -

l0 0 --/~ ........ ..... ...... ...........

0 k W "'""..""" ....... "".. .-. 10-1 "....... ...-.'..

10.2 . i , , . J . . L , , . i , . , 2 4 6 8

VER (kW)

Fig. 8. Energy spectra of the end-loss electrons measured with the LED. The values 0 - 1 5 0 k W denote the plug E C R H power.

10

T. Saito et al. / Fusion Engineering and Design 26 (1995) 241 250 247

ing into the collector of the LED is plotted as a function of the electron repeller voltage VER- The collector is connected with the machine ground through a low resistance. Both the flux and the mean energy increase with increase in the plug ECRH power Pplug. The energy spectra of the end-loss electrons cannot be expressed with a single component Maxwellian, but they are well fitted to a two-component Maxwellian:

V E R -~- (1)Ep VER ~-- (I)Ep exp( ~/'TH. -)

for VER ~> IOEp](OEp < 0). Here, TeL denotes the temperature of the bulk component and Tell is that of the high-energy tail component. The value of Ie is almost constant for VER ~< I@Ep] because the end plate effectively works as an electron repeller. With these parameters an effective temperature T~, is defined as a measure of the mean energy:

Ten" = (1 - fl)TeL + flTeH

where fl is the flux fraction of the Tell component to the total flux: fi = IH/(I L + In). Here, # is evaluated at VeR = [@EP[. The dependence of Tefr on Pplug is presented in Fig. 9(a). The effective temperature T~er increases almost linearly with Pplug. This is one of scalings that express strong effects of the plug ECRH. This scaling has a very impor- tant meaning in the study of potential formation [9,10].

Since the LED measures the electron flux behind the end plate, the measured flux is reduced by the negative potential of the end plate. In Fig. 9(b) the flux is plotted as a function of Pp~ug after multiplication by a factor of exp([@~pl/eT~L ). Then it represents the electron flow driven out of a plasma. The flux drastically increases even for a low power and then gradually increases with increase in P p l u g - By using the profile shown in Fig. 7 and further assuming axisymmetry, a rough estimation of the total out-flux gives a few tens of amperes. However, secondary electrons emitted from the end plate ensure the charge balance [6]. Naturally, the magnitude of the driven current strongly depends on plasma parameters even for the same heating power.

[..

1.5

0.5

(a)

8 0 0 0

50 100 150 200

Pp,.,(kW)

10'

~.~ 10 ° E

10-'

. . . . i

(b)

8 o 0

o 8

#110863~948 T=70ms, 90ms

] 0 . 2 . . . . I ' , i I I i i i i I i i i ,

0 50 100 150 200

Pp,o, (kW)

Fig. 9. (a) effective temperature Teer and (b) flux 1~ plotted as functions of the plug ECRH power Pp~ug.

The energy spectrum of high-energy electrons has been measured by the SSB detector. The low-energy side of the measured spectrum is con- tinuous with the Tell component of the spectrum measured with the LED. On the other hand, the high-energy side extends to about 500 keV [10].

4.2. Diffusion of electrons & velocity ,space

We compare the strength of heating with that of the collisional process. The heating time associated with the fundamental ECRH and the drag time due to cold electrons are appropriate figures for comparison. The heating time rh is defined as

l" h = - r b /

by using the average energy gain (AW) per bounce time %. We use an equation for r h derived from a quasiqinear heating model [22]. By apply-


ing the model to the present geometry the following expression is obtained:

Zh = Tow 4rnf~°l e2E+2L tan ~ 0

where E+ is the electric field of the right-hand circularly polarized wave, ~o is the cyclotron frequency at the mid-plane, L = 1/B(dB/dz) is the magnetic field scale length at the resonance position, l = 1/B(d2B/dz 2) is that at the mid-plane and 0 is the pitch angle of the resonant electron evaluated at the mid-plane. Here, the warm electron temperature Tew is identified with the mean energy of the resonant electrons. The collisional relaxation is represented by the drag time rd estimated from the following equation [23]:

Zd(S ) =2.1 × 10 4 Tew3/2

H e

(Tow in eV, ne in cm-3), where n e is the back- ground cold electron density.

Fig. 10 plots conditions of rh/Zd = 1 for various Tew. Because electrons confined by the end plate potential interact with cold electrons also in the central region, a factor, which is the ratio of the length of the confinement region to that of the end cell, is multiplied in the evaluation of rh/ro. On the upper side of the curves Zh is smaller than z~. The electric field associated with the funda-

1 0 3

1o 2

. . . . . . . . i . . . . . . . .

~:~---Tew = 30eV

[] 300eV o 3000eV

1 0 1 . . . . . . . . i . . . . . . . .

1011 1012 1013

n e (era "3)

Fig. 10. Curves expressing the relation Zh/'~ d = 1 for different warm electron temperatures. The pitch angle is assumed to be 45 ° .

mental ECRH is 200-500 V c m - l and the electron density is lower than (2-4) × 1012 c m -3 in the present experiment. Therefore, resonance heating is stronger than collisional relaxation.

A representation of the diffusion of electrons in velocity space is given in Fig. 11. The magnetic field and the potential profile from the end cell to the end plate are illustrated in Fig. l l(a). The velocity space of electrons is expressed in Fig. l l (b) by using the energy e and the magnetic moment p. Electrons below the line ~ = # B c -e@Ep is confined by the end plate potential and those below the line e = ~ B m - e ( I ) m are magneti- cally confined. The shaded area represents the loss region. Arrows in the figure stand for the direction of diffusion along heating characteristics

(a) Magnetic Field

Potential Bm

End Plate • t .~ Electrons < .~ -.~

(b)

-et]DEP

0

-e~m

(II)

-Drive by ECRH

~e=gBc-eq~EP

Fig. 11. (a) Schematic diagram of the axial profiles of the magnetic field and the potential; (b) velocity space expressed with the energy e and the magnetic moment #.

T. Saito et al. / Fusion Engineering and Design 26 (1995) 241 250 249

which are defined as e =/~Bp + e 0 with a parame- ter n0 [24,25]. Electrons are promptly lost when they are transferred by a small pitch angle, scat- tering to the velocity space region where heating characteristics are connected to the loss region.

The mechanism which causes the observed energy spectrum of the end-loss electrons has not been fully understood. However, a F o k k e r - Planck code developed to study the heating process of electrons by E C R H in a mirror field [26] partly reproduces the observed spectrum. The code calculates the energy distribution of the electrons which pass the loss cone boundary. Fig. 12 plots calculated energy distributions in the energy range lower than 20 keV. The calculation does not include the potential effect. Therefore, we can compare the calculated distribution with the ex- perimentally obtained one only in the energy range higher than the electron confining potential ( 2 - 3 keV). The energy distribution in this range is similar to the Ten component of the end-loss electrons and the calculated flux is very small in the absence of the fundamental ECRH. These features are consistent with observations.

The geometry of the plug region is similar to the scheme of current drive in a toroidal machine by using E C R H proposed by Parks and Marcus [27]. The idea is based on transformation of the magnetic moment given at the heating point to

the parallel momentum making use of the magnetic field gradient along a field line.

5. Conclusion

We have examined hot electron production in the anchor cell and the generation of the electron flow. Hot electrons with a/~ value larger than 20% have been produced for the case with centre resonance. The spatial profile of the hot electrons depends on the location of the resonance surface. This stems from the heating configuration of our experiment. We can produce hot electrons with various spatial profiles, which are useful in examining the effects of hot electrons on M H D stability.

Fundamental E C R H generates an intense flux of end-loss electrons. The loss flux contains multi- components and extended to 500 keV. However, most of the loss flux is composed of warm electrons with energies from several hundred eV to a few keV and this part of the end-loss flux is of significance for the potential formation in G A M M A 10. The effective temperature as a measure of the mean energy of the warm electrons is proportional to the E C R H power. In the present experiment, diffusion of electrons in velocity space due to resonance heating is much stronger than the collisional relaxation.

100

10-1

10-2

10-3

10 .4

I0-S

10-6

10-7

lO-S

. . . . i . . . . i . . . . i . . . .

O 0 ©

200V/c m D D 0 0 0 0 0 0 0 0 0 0 0

D D 0 50 Vlcm

X [] [] X ~000

0 ~ ×

X 0 V/cm

X i , i , I i , , , I , , , i I , , i h

5 10 15 20 E (keV)

Fig. 12. Energy spectra of the electrons passing the loss cone boundary of the end mirror cell calculated by the Fokker Planck code for different wave electric fields.

Acknowledgement

The authors express their gratitude to the mem- bers of the G A M M A 10 group for their collabo- ration and valuable discussions in the course of the present study.

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Electron cyclotron resonance heating experiments in the GAMMA 10 tandem mirror