RADIO-FREQUENCY HEATING IN STRAIGHT

FIELD LINE MIRROR NEUTRON SOURCE

V.E.Moiseenko1,2, O.Ågren2,

K.Noack2

1 Kharkiv Institute of Physics and Technology, Ukraine2 Uppsala University, Sweden

OUTLINE

• SFLM FDS• Scenarios for ICRH• Numerical model• Parameters of calculations• Calculation results• Conclusions

SFLM FDS

Fusion

Fission reactor

Background plasma

Mirror part

Hot ions

RF antennas

Usage of a SFLM is beneficial to localize the fusion neutron flux to the SFLM part of the device which is surrounded by a fission mantle. The device would be capable to operate continuously.It is expected that full control on plasma could be achieved.The device is relatively simple.

Scenarios for ICRH

plasma

FMSW cut-off

Alfven resonance cut-off

Deuterium cyclotron surface

Conversion surface

FMSW FAW FMSW

antenna

Minority heating:

Wave is launched by antenna near ut-off

Wave does not propagates to high field side reflecting from cut-off

FMSW then converts to FAW

Alfven resonances are also excited

FAW is absorbed owing to cyclotron damping

Second harmonic heating:

The same, but no conversion to FAW and no Alfven resonances

Conversion to IBW is possible

RF field forms a standing wave in radial direction and propagates along magnetic field towards midplane

V.E. MOISEENKO, O. AGREN, Phys. Plasmas 12, ID 102504 (2005).V.E. MOISEENKO, O. AGREN, Phys. Plasmas 14, ID 022503 (2007).

Scenarios for ICRH (cont.)

(a)

(b)

(c)

(d)

(e)

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4100.00 4150.00 4200.00 4250.00 4300.00 4350.00 4400.00 4450.00 4500.00

z [cm ]

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720.00 740.00 760.00 780.00 800.00 820.00 840.00 860.00 880.00 900.00

z

-20.00

0.00

20.00

x

-20.00

0.00

20.00

x

Power

Re Ex

Im Ex

Re Ey

Im Ey

The SFLM neutron source has a substantially smaller size than a fusion reactor machine. In this situation the fast magnetosonic wave which is excited by the antenna makes fewer oscillations across the magnetic field.

The width of the ion cyclotron zone becomes smaller owing to the sharper gradients of the magnetic field magnitude along magnetic field lines.

The last factor is softened by a smaller mirror ratio.

Reactor Neutron sourceSecond harmonic calculation

Numerical model

extik jEεEeeE 020|||| ˆ

Zero electron mass approximation is chosen in which the parallel component of the electric field is neglected in Maxwell’s operator

)exp(

2)(1 2

||||

2i

Fvk T

p

WKB formulas for cyclotron damping: fundamental harmonic

||||/ Tc vk,

Second harmonic

EeEeEeeD ||22||2||||0~

4

1~8

1~8

1/ i

)1/)(/21(1)exp(2

)(4~ 2

||22

222||||

22

2

TTc

cT

Tp vvi

Fvk

v

||||2 /2 Tc vk V.E. MOISEENKO, O. AGREN, Phys. Plasmas 14, ID 022503 (2007).

0nEBoundary conditions

0)()(

zwz ikz

eEeE

Parameters of calculations

In the numerical calculations, the following regular set of parameters is chosen: Plasma density (in its maximum) is

14

0 10en cm-3, heating frequency is 8101.21.1 s-1, deuterium and tritium parallel and perpendicular thermal velocities at the z -axis are 5

|||| 105 TTDT vv m/s and 61035.1 TTDT vv m/s, the deuterium concentration is

4.0DC , 2.0|| k cm-1 and 15.0wk cm-1.

We choose the antenna height as 9xl cm, the antenna width as 10zl cm and the antenna length as 130yl cm. The regular

position of the antenna with respect to the center of the trap is 845az cm.

Calculation results (minority heating)

1E+8 1.2E+8 1.4E+8 1.6E+8

0

4

8

12

16

20

2/2 IPr displ

dVEpPdis

Im2

202 sΠΠ dPfl )( 2

flpltot rrr

Dependence of the absorption (solid line) and shine-through (dashed line) resistances on RF heating frequency.

6E+13 8E+13 1E+14 1.2E+14 1.4E+14

0

4

8

12

16

20

Dependence of the absorption and shine-through resistances on plasma density.

Calculation results (minority heating)

840 860 880 900 920

0

10

20

30

Dependence of the absorption and shine-through resistances on antenna location.

Calculation results (second harmonic heating)

1.4E+8 1.6E+8 1.8E+8 2E+8 2.2E+8

0

4

8

12

16

20

Dependence of the absorption (solid line) and shine-through (dashed line) resistances on RF heating frequency.

6E+13 8E+13 1E+14 1.2E+14 1.4E+14

0

4

8

12

16

20

Dependence of the absorption and shine-through resistances on plasma density.

Calculation results (second harmonic heating)

840 860 880 900 920 940

0

10

20

30

7E+7 8E+7 9E+7 1E+8 1.1E+8

0

4

8

12

16

20

Dependence of the absorption and shine-through resistances on antenna location.

Dependence of the absorption and shine-through resistances on tritium thermal velocity.

CONCLUSIONS• The calculations indicate good performance of deuterium minority heating

at fundamental ion cyclotron frequency. • The heating is weakly sensitive to the ion temperature and, therefore, has

no start-up problem. • The sensitivity to other factors, e.g. plasma density, antenna location etc.,

is not critical.

• The second harmonic heating of tritium is more delicate. It is every time accompanied by a noticeable shine-through of the wave energy to the middle part of the trap where the wave would be absorbed by the deuterium at the second harmonic ion cyclotron zone.

• Most of the remaining wave energy may also be absorbed at the second harmonic tritium resonance zone near the opposite mirror.

• The calculations predict relatively sensitive dependence on plasma density, antenna location and tritium temperature. However, if the necessary conditions are provided this heating is satisfactorily efficient.