Transcript Stellarator-mirror based fusion driven fission reactor

PLASMA HEATING AND HOT
ION SUSTAINING IN MIRROR
BASED HYBRIDS
1,2
V.E.Moiseenko ,
1
2
O.Ågren ,
Kharkiv Institute of Physics and Technology, Ukraine
2 Uppsala University, Sweden
OUTLINE
• SFLM AND STELLARATOR-MIRROR
FDS
• SCENARIOS FOR NEUTRON SOURCE
• NUMERICAL MODEL FOR NBI
• CALCULATION RESULTS FOR NBI
• SCENARIOS FOR ICRH
• NUMERICAL MODEL FOT ICRH
• CALCULATION RESULTS FOR ICRH
• CONCLUSIONS
SFLM AND STELLARATOR-MIRROR
Stellarator-mirror
FDS
SFLM
NBI
Hot
ions
Fission
reactor
Fission
reactor
Neutron
capturer
Fusion
neutron flux
Fusion
Background plasma
Stellarator
part
nd plasma
RF antennas
Mirror part
ror part
Magnetic coils
Usage of a open trap for hot ion confinement is
beneficial to localize the fusion neutron flux to
the SFLM part of the device which is surrounded
by a fission mantle.
The devices would be capable to operate
continuously.
It is expected that full control on plasma could
be achieved.
SCENARIOS FOR NEUTRON
SOURCE
Two scenarios of discharge arrangement in mirrors are of interest for the
fusion neutron source. Both take advantage of mirror trapping of high
energy ions.
•In the first scenario one ion component is hot, and
neutrons are produced in collisions with the background
plasma ions which are in thermal equilibrium with the
electrons.
•In this scenario the power balance is determined by the
electron drag: The power PTe-3/2 for the ion heating
decreases with an increase of the electron temperature.
•Additional heating of electrons, e.g. with
cyclotron heating, is less practical because
heating could be achieved by increasing the
population, which also increases the fusion
output.
electron
electron
hot ion
neutron
In the second scenario, both deuterium
and tritium ions are hot.
The background plasma is sustained to
stabilize plasma instabilities caused by
the non-equilibrium (loss-cone) velocity
distributions of the hot ions.
Here, the role of the electrons in power
balance is less accentuated, and
electron heating would be less
important.
A key problem for the two mentioned scenarios of discharge is hot
ion sustaining. This could be made with neutral beam injection
(NBI) or radio-frequency (RF) heating in the ion cyclotron range
of frequencies.
NUMERICAL MODEL FOR NBI
1.
The stationary kinetic equation for fast ions reads:
f
f
v ||
 Ccol ( f )   I inj
l

2.
3.
In the model it is assumed that the hot ions are in minority
and collisions of hot ions with themselves are ignored.
Another assumption is smallness of the particle drift
excursion in perpendicular to the magnetic field direction
during collision time.
This assumption allows one to consider velocity
distributions separately at each magnetic field line and
ignore particle perpendicular motion.
For Maxwellian plasma the collision operator is
Ccol ( f )     v  F
  e ,i
.
and
indices hi and =e,i denote hot ions, electrons and
background ions respectively


mhi
1
1
2
F
 s vf   || vv   v f    v  v f  vv   v f
mhi  m
2
4
2
m
v
2 2

4ehi e n
x
   21  1/(2x)   0  0 
2k
T
2 3
B

mhi v
 ||   0 / x
x
2

 s  (1  mhi / m ) 0
 t exp(t )dt

0
NUMERICAL MODEL (cont.)
f  f ( ,  )
If (collision time)/(bounce time)>>1
v||0  2  B0  / mhi
v 0  2B0 / mhi
New variables :
Bounce averaging
 dl 


 l v|| 
l 
1
 dl 


 l v|| 
l 
1
lr
lr
lr

C
col
( v || 0 )  f /  ( v || 0 )  Ccol ( v|| 0 )  f /  ( v || 0 )dl
v||
ll
lr

ll
I
inj


( v || 0 )  I inj ( v|| 0 ) dl
v ||
In the code, time is expressed in units of ion-ion collision time for the
background ions. The velocity is normalized by the background ion thermal
velocity.
CALCULATION RESULTS
Regular parameter set:
Normalized perpendicular velocity
8
7
Einj  Einj /(kBT )  100  mir  100  st  1
magnetic field depends parabolically on the longitudinal coordinate
the mirror ratio is chosen as R=1.7, NBI
generates ions with perpendicular energy at
3.4
3.2
R=1.3. NBI energy spread is chosen as E
3.0
2.8
6
2.6
2.4
5
2.2
2.0
4
1.8
1.6
3
1.4
1.2
1.0
2
0.8
1
For this parameter set the average normalized ion
energy is E  34
hi
The electron drag takes 62% of the injected power, the
ion-ion collisions 19%. The remainder goes to the loss
cone and is lost due to finite confinement time at the mirror
part of the device.
0.6
1
0.4
A change of the mirror ratio from R=1.7 to R=2
increases the hot ion content only by 1%, and the
Normalized parallel velocity
Contours of distribution function. mean ion energy also remains almost unchanged.
0.2
1
2
3
4
5
6
Dashed line shows boundary
between trapped and passing
particles.
CALCULATION RESULTS (cont.)
An increase of the ion confinement time at the mirror part from
to
 mir  1000
 mir  100
results in a hot ion density increase by 10%, and this value
does not change significantly with further increase of this parameter.
Confining properties of the stellarator are also not very sensitive: A decrease of the
 st  1 to  st  0.3
stellarator confinement time from
results only in a decrease of hot ion population by 4%.
Neutron emission line
intensity for Einj=300keV
and two different
background plasma
temperatures.
Einj=200
Einj=100
Fusion Q
0,6
0,4
0,2
0
0
2
4
6
Background temperature, keV
Dependence of fusion Q on
background plasma temperature for
two normalized injection energies.
Netron flux line density, a.u.
0,8
T=3 keV
T=0,8 keV
-1,5
-1
-0,5
0
0,5
Norm alized length
1
If the fission mantle is
located at |l|<0.5, the
relative portion of the
neutrons emitted in this
zone is 61% for T=3
keV and 57% for T=0.8
keV.
1,5 If -0.5<l<1 this portion
rises to 80%
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 cut-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
20.00
(a)
0.00
-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
Im Ey
4500.00
z [cm]
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
z
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.
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  k εˆ  E  i0 jext
2
0
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
Plasma radius at the central plane where the magnetic surfaces
have a circular cross-section is a=40 cm, magnetic field value at
the midplane is B0=2 T, the trap length is L=18 m and the mirror
ratio at the trap ends is R=2.3.
We choose the antenna height as l x  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
z a  845cm.
In the numerical calculations, the following regular set of
parameters is chosen: Plasma density (in its maximum) is
-3
frequency is   1.1  2.1  108 s-1,
ne 0  1014 cm , heating
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  106 m/s, the deuterium concentration is
CD  0.4 , k||  0.2 cm-1 and k w  0.15 cm-1 .
CALCULATION RESULTS
(MINORITY HEATING)
rpl  2Pdis / I
2
rtot  rpl  r fl
2
 0


Pdis   p2 
E Im  dV Pfl  (Π  Π 2 )  ds
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
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
•
Hot ion sustaining is most important for mirror and stellarator-mirror
fission-fusion hybrid devices. Efficient methods for this are NBI and ion
cyclotron resonance heating.
•
According to the numerical results for NBI in a stellarator-mirror hybrid,
the hot ion population depends only weakly on the confinement of the
stellarator part.
•
At the mirror part, it is sufficient to confine the hot ions for only a
few hot ion-background ion collision times.
•
The mirror ratio of the local mirror trap which is sufficient to avoid
substantial ion losses is small, a value R=1.7 is adequate, and increasing
it does not result in a considerable increase of the hot ion population.
•
The calculated axial distribution of the neutron flux peaks at the
injection points and has a noticeable magnitude at locations between the
peaks. About 60% of the flux reaches the fission mantle if the NBI is made
from both sides of the nuclear core. This amount rises to 80% for singleside NBI. It could be further increased by a steeper magnetic field
profile near the injection area and making the field more uniform in the
remaining mirror part.
CONCLUSIONS (cont.)
•
The calculations for the straight field line mirror hybrid show
good performance of deuterium minority heating at the
fundamental ion cyclotron frequency. The heating is not strongly
dependent on 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.
•
Second harmonic heating of tritium is always accompanied by a
noticeable shine-through beyond the tritium second harmonic
resonance zone. However, the wave power would not be wasted,
since the shined-through wave encounters deuterium second
harmonic cyclotron resonance on its way to the midplane. Most of
the remaining small wave energy may also be absorbed at the
tritium second harmonic resonance zone near the opposite mirror.
•
The second harmonic heating 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.
Thank you!