Possible further steps for upgrading the GDT device

1
Possible further steps for upgrading the GDT
device
T.D. Akhmetov, A.A. Ivanov, and V.V. Prikhodko
Budker Institute of Nuclear Physics, Novosibirsk,
Russia
2
Outline

• Current parameters of Gas Dynamic Trap (GDT)
• Why upgrade?
• to increase electron temperature and hot ion
  energy content
• to optimize magnetic field
• to improve MHD stability
• Possibilities
• proceed from 5 to 20 ms neutral beam injection
• adjust the present coil system
• add coils to enhance magnetic field from 3.3 to
  4.5 kGs

3
GDT layout
Length 7 m Magnetic field
center up to 0.33 T
mirror up to 15 T Mirror ratio
up to 35 Injection duration 5
ms NBI power up to 5 MW
Warm plasma (2-3)?1013 cm-3, 200 eV Hot ions
(H, D) up to 51013 cm-3, ltEgt10 keV
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Typical experimental scenario

• Cusp and expander are not used
• MHD stability is provided by a biased limiter
• Gas puffing maintains warm plasma density

NB injection
Gas puffing
Plasma source
0.5
3.5
8.5
t, ms
5
Incident NBI power
Injection energy Einj 22?25 keV
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D0 injection into D plasma
Hot ion diamagnetism with D0 injection into D
plasma (B0 0.33 T, R 32)
dWf /dt ? 0.4 kJ/ms
By the end of injection n ? 5?1013 cm?3 and Te ?
180 eV ? for deuterons ?ei
? 4 ms No steady
state yet
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Electron temperature at the axis
Te , eV
No steady state yet
t, ms
Experiment Wf and Te are not saturated at 5 ms
NBI Proposal extend injection up to 20 ms to
increase Wf and Te
Optimistic estimation without ? limit
max(Wf) ? 0.4 kJ/ms
?20 ms ? 8 kJ
8
Search for steady state

• Zero-order (space-averaged) numerical model
  includes
• kinetic equation for hot ion distribution
  function fhi(e)
• particle balance equations for warm ions and
  electrons nwi, ne
• energy balance equations for electrons and warm
  ions Twi, Te
• NB injection, gas puffing, and axial gas-dynamic
  plasma losses

The model was adjusted to reproduce Te(t) and
Wf(t) for 5 ms injection in the current
experiments.
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Numerical simulation for 5 ms injection
Calculation ne 1014 cm?3, Pinj 4 MW
Experiment
Te , eV
t, ms
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Increase of injection pulse length
Our simple numerical model gives qualitative
agreement with experiments for small and large
gas puffing for 5 ms NBI. Now the model is
developed to better account for cold halo plasma
and balance of neutral gas in order to proceed
to 20 ms regime.
??60 already and storage of hot ions will be
limited soon by ballooning instability. Therefore
, extension of the injection pulse together with
magnetic field increase should allow accumulation
of significantly greater hot-ion energy content
which in turn should allow for greater Te.
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Outline

• Current parameters of Gas Dynamic Trap (GDT)
• Why upgrade?
• to increase electron temperature and hot ion
  energy content
• to optimize magnetic field
• to improve MHD stability
• Possibilities
• proceed from 5 to 20 ms neutral beam injection
• adjust the present coil system
• add coils to enhance magnetic field from 3.3 to
  4.5 kGs

12
Plasma ? near the turning point
Estimation from magnetic field depression ?max
? 0.6
Hot ion density estimation near the turning point
lt e gt 10 keV ? n ? 5?1013 cm?3
Value of ? is close to the ballooning instability
limit in GDT (?crit 0.7?0.8) and will limit
hot ion accumulation and electron heating. Can
we decrease ? near the turning point keeping the
same or even larger Wf ? Since ? ? phi /B2, to
increase Wf ? ? phidV , one has to increase B or
reduce hot-ion pressure near the turning point.
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Length of hot-ion turning region
Let us change angle by ?? and calculate the shift
of the turning point

• Hot-ion pressure near the turning region can be
  reduced by increasing the volume of this region,
  i.e. its length.
• Either angular spread of hot-ion D.F. must be
  increased or magnetic field gradient must be
  reduced near the turning point.
• Angular spread cannot be increased much,
• Magnetic field gradient dB/dz(zs) can be
  increased by correction of currents in the
  coils or their positions near the turning point.

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Hot-ion population in GDT
For n5?1013 cm?3, Te200 eV, Ei 20 keV
ion energy loss
ms for H and 4.8 ms for D
ion scattering
ms for H
Thus, scattering can be neglected during the
whole plasma pulse length. In simple estimations
we will neglect also deceleration of ions on
electrons Hot-ion (neutral beam) distribution
function is taken in the form
?0 ? injection energy ?0 ? pitch-angle of
injection ?? angular width
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Hot-ion density and pressure distributions
Peaking of density and pressure near the turning
point relative to the central plane
For ?? ltlt ?01
In GDT ?045? p(zs)/p(0) 5.2 ???1/2
degree and for ??5? p(zs)/p(0) 2.3
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Reduction of pressure in the turning region
Multiplier for the coil current
1.7
1.22
0.8
0.48
b(z)
b(z)
corrected
z, cm
z, cm
turning point
now
p(z)
corrected
r??/rB2
z, cm
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Effect of coil current correction

• limit in the hot-ion turning region can be
  significantly improved by reducing the peak
  plasma pressure 1.5 times using correction of
  the coil currents.
• It should increase the hot-ion energy content Wf
  possible for the given magnetic field strength.

18
Outline

• Current parameters of Gas Dynamic Trap (GDT)
• Why upgrade?
• to increase electron temperature and hot ion
  energy content
• to optimize magnetic field
• to improve MHD stability
• Possibilities
• proceed from 5 to 20 ms neutral beam injection
• adjust the present coil system
• add coils to enhance magnetic field from 3.3 to
  4.5 kGs

19
MHD flute stability criterion
Assumptions ?8?p/B2 ltlt 1 axial symmetry
paraxial limit, a2/L2ltlt1
Plasma is stable if variation of potential energy
of perturbations is positive
For radially localized perturbations and for
sharp boundary plasma (M.N.Rosenbluth,
C.L.Longmire, 1957)
? field line curvature
Advantages ? simplicity, clearness
Disadvantages ? paraxial limit (fails in the
turning region) ? small ? (fails in the turning
region) ? applicable only for small-scale modes
or for p(r) const and sharp boundary
We will use this criterion as a starting point
for estimations of MHD stability
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Optimal B(z) profile for GDT with p(z)const
For p(z)const, W is minimal forBushkova,
Mirnov, Ryutov, 1986
r, cm
b(z)?10
z, cm
Magnetic field was originally optimized for
pconst
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More realistic p(z) profile
Now pressure is strongly anisotropic due to
sloshing ions
p
r''/rB2
pr''/rB2
unfavorable curvature, r''lt0
z,cm
R2, turning point for ions injected at 45?
Magnetic field should be corrected to reduce
unfavorable curvature. It will improve MHD
stability.
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Corrected coil positions in GDT
Minimization of potential energy W with pp(B)
for sloshing ions by shifting several coils
reduces W by a factor of 2.7 compared to the
present GDT system
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Corrected coil positions in GDT
pr''/rB2
pGDT
corrected
GDT
z,cm
Relatively simple adjustment of coils can improve
MHD stability
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Outline

• Current parameters of Gas Dynamic Trap (GDT)
• Why upgrade?
• to increase electron temperature and hot ion
  energy content
• to optimize magnetic field
• to improve MHD stability
• Possibilities
• proceed from 5 to 20 ms neutral beam injection
• adjust the present coil system
• add coils to enhance magnetic field from 3.3 to
  4.5 kGs

25
Increase of magnetic field
Additional coils from AMBAL-M with I26.3 kA
placed optimally to provide the same B(z)
profile as in GDT, increase magnetic field in
the central cell 1.36 times over the length
?260ltzlt260 cm (turning points zt ?190 cm) up to
4.5 kGs. These coils can be fed by available
capacitor storage of the GOL device.
Increase of B will allow accumulation of hot-ion
population with greater energy content Wf and
further increase of Te
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Conclusions

• 20 ms NBI together with magnetic field increase
  should provide steady state with significantly
  enhanced Wfast and Te
• Proposed experiment with lengthening of hot-ion
  turning region may give additional information
  about ? limit and increase Te
• Adjustment of the present coil system may
  significantly improve MHD stability
• Increase of central cell magnetic field by a
  factor of 1.36 is possible with available
  additional coils and capacitor storage

A.A. Ivanov Perspectives of development of
magnetic mirror traps in Novosibirsk Friday,
July 9 1210