Transcript Stellarator-mirror based fusion driven fission reactor

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, Ukraine
2 Uppsala University, Sweden
OUTLINE
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SFLM FDS
Scenarios for ICRH
Numerical model
Parameters of calculations
Calculation results
Conclusions
SFLM FDS
Hot
ions
Fission
reactor
Fusion
Background plasma
RF antennas
Mirror part
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
Deuterium
cyclotron
surface
FMSW
Conversion
surface
FAW
FMSW
cut-off
FMSW
RF field forms a standing
wave in radial direction
and propagates along
magnetic field towards
midplane
Minority heating:
plasma
antenna
Alfven
resonance
cut-off
Second harmonic heating:
The same, but no conversion to FAW and
no Alfven resonances
Conversion to IBW is possible
V.E. MOISEENKO, O. AGREN, Phys. Plasmas 12, ID 102504 (2005).
V.E. MOISEENKO, O. AGREN, Phys. Plasmas 14, ID 022503 (2007).
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
Scenarios for ICRH (cont.)
Second harmonic calculation
Reactor
Neutron source
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(a)
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-20.00
Power
x
x
20.00
0.00
-20.00
20.00
(b)
0.00
-20.00
Re Ex
x
x
20.00
0.00
-20.00
20.00
(c)
0.00
-20.00
Im Ex
x
x
20.00
0.00
-20.00
20.00
(d)
0.00
-20.00
Re Ey
x
x
20.00
-20.00
20.00
(e)
0.00
-20.00
4150.00
4200.00
4250.00
4300.00
4350.00
4400.00
4450.00
4500.00
Im Ey
x
x
20.00
4100.00
0.00
0.00
-20.00
720.00
740.00
760.00
780.00
800.00
820.00
840.00
860.00
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.
z [cm]
z
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.
880.00
900.00
Numerical model
Zero electron mass approximation is chosen in
which the parallel component of the electric
field is neglected in Maxwell’s operator

Boundary conditions
E n  0

(E  e z )  ikw (E  e z )  0
z

    E  e||e||  E  k02εˆ  E  i 0 jext
WKB formulas for cyclotron damping: fundamental harmonic
   1  

 p2
 k|| vT ||


i 
2
exp(    ) ,
 F ( ) 
2


    c  / k|| vT ||
Second harmonic
1
1
1 ~
~
~
D /  0   e||  e||       2   E   ie||       2   E     2  e||   E 
8
8
4
2
2


4

v
i 
p T 
2
2
2
~
 2  
F
(

)

exp(


)

1

(
1

2

/

)(
v
/
v

2
2 
c
T 
T ||  1)
2
2

  k||vT || c 


 2    2c  / k|| vT ||
V.E. MOISEENKO, O. AGREN, Phys. Plasmas 14, ID 022503 (2007).

Parameters of calculations
We choose the antenna height as lx  9 cm, the antenna width
as l z  10 cm and the antenna length as l y  130 cm. The regular
position of the antenna with respect to the center of the trap is
za  845 cm.
In the numerical calculations, the following regular set of
parameters is chosen: Plasma density (in its maximum) is
-3
8 -1
14
ne 0  10 cm , heating
frequency is   1.1  2.110 s ,
deuterium and tritium parallel and perpendicular thermal
velocities at the z -axis are vT||D  vT||T  5105 m/s and
vT D  vT T  1.35  10 6 m/s, the deuterium concentration is
-1
-1
CD  0.4 , k||  0.2 cm and k w  0.15 cm .
Calculation results (minority heating)
rpl  2Pdis / I
2
rtot  rpl  r fl
2
 0


Pdis    p2 
E Im   dV
2


20
20
16
16
12
12
8
8
4
4
0
0
1E+8
1.2E+8
1.4E+8
1.6E+8
Dependence of the absorption (solid
line) and shine-through (dashed line)
resistances on RF heating frequency.
6E+13
8E+13

Pfl  (Π  Π 2 )  ds
1E+14
1.2E+14
1.4E+14
Dependence of the absorption and shinethrough resistances on plasma density.
Calculation results (minority heating)
30
20
10
0
840
860
880
900
920
Dependence of the absorption and shine-through resistances on antenna location.
Calculation results (second harmonic
heating)
20
20
16
16
12
12
8
8
4
4
0
0
1.4E+8
1.6E+8
1.8E+8
2E+8
2.2E+8
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
Dependence of the absorption and shinethrough resistances on plasma density.
Calculation results (second harmonic
heating)
30
20
16
20
12
8
10
4
0
840
860
880
900
920
940
Dependence of the absorption and
shine-through resistances on
antenna location.
0
7E+7
8E+7
9E+7
1E+8
1.1E+8
Dependence of the absorption and
shine-through resistances on tritium
thermal velocity.
CONCLUSIONS
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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.