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

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

GDT layout

Length: 7 mMagnetic field: center up to 0.33 T mirror up to 15 TMirror ratio: up to 35Injection duration: 5 msNBI power: up to 5 MW

Warm plasma:

(2-3)1013 cm-3, 200 eV

Hot ions (H+, D+):

up to 5·1013 cm-3, <E>≈10 keV

Typical experimental scenario

Plasma source

Gas puffing

NB injection

0.5 3.5 8.5 t, ms

• Cusp and expander are not used

• MHD stability is provided by a biased limiter

• Gas puffing maintains warm plasma density

Incident NBI power

Injection energy Einj = 2225 keV

D0 injection into D plasma

By the end of injection n 51013 cm3 and Te 180 eV

for deuterons ei 4 ms

No steady state yet

Hot ion diamagnetism with D0 injection into D plasma (B0= 0.33 T, R = 32)

dWf /dt 0.4 kJ/ms

t, ms

Te , eV

Electron temperature at the axis

No steady state yet

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

Search for steady state

Zero-order (space-averaged) numerical model includes• kinetic equation for hot ion distribution function fhi()

• 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.

Numerical simulation for 5 ms injection

Calculation: ne = 1014 cm3, Pinj = 4 MW

Experiment

t, ms

Te , e

V

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.

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

Estimation from magnetic field depression: max 0.6

Hot ion density estimation near the turning point

2

8,

V

n

B

< > = 10 keV n 51013 cm3

Plasma near the turning point

Value of is close to the ballooning instability limit in GDT (crit ~ 0.70.8) 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.

Length of hot-ion turning region

0

02sin

)(

1

BzB s

Let us change angle by and calculate the shift

of the turning point

0

0

sin

cos2

)(

)(

s

ss

zdzdB

zBz

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.

Hot-ion population in GDT

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

4.224

34

23

nem

Tm

e

eiEie

402 4

23

ne

Em iiii

For n~51013 cm3, Te~200 eV, Ei ~ 20 keV

ms for H+ and 4.8 ms for D+

ms for H+

))(exp()(),( 22000 ff

ion energy loss

ion scattering

0 injection energy

0 pitch-angle of injection

angular width

Hot-ion density and pressure distributions

B

ddf

m

BVd

Vmzp

ddBfm

BVdmVzp

B

ddf

m

Bzn

23

23

2

2332

||||23

22

2)(

,24

)(,22

)(

For << 0~1

1

cos1

1

sin

cos45

2

)0(

)(

,1

sin

cos45

2

)0(

)(

02

03

0

03

0

p

zp

n

zn

s

s

In GDT 0=45 p(zs)/p(0) ~ 5.2 1/2 [degree] and for =5: p(zs)/p(0) ~ 2.3

Peaking of density and pressure near the turning point relative to the central plane

0 50 100 150 200 250 300 350 4001

0

1

104

_rB2l

80 p_05_equali

80 p_05_cor i

zz l zi zi

0 50 100 150 200 250 3000

1

2

3

4

5

Bz_GDT_norm l

b zz l Bz_GDT_norm_cor l

zz l

0 50 100 150 200 250 300 3500

10

20

30

40

50

60

70

rcj

10 Rmirl

10 b zz l

zc j zz l zz l

1.7

Multiplier for the coil current

1.22 0.8 0.48

p(z)

Reduction of pressure in the turning region

b(z)b(z)

z, cm

z, cm

z, cm

r/rB2

corrected

corrected

now

turning point

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.

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

MHD flute stability criterion

Assumptions: =8p/B2 << 1; axial symmetry; paraxial limit, a2/L2<<1

– field line curvature

For radially localized perturbations and for sharp boundary plasma(M.N.Rosenbluth, C.L.Longmire, 1957)

||ppp

02

dz

rBpW

Plasma is stable if variation of potential energy of perturbations is positive

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

0 50 100 150 200 250 300 3500

10

20

30

40

50

60

70

rcj

10 Rmirl

10 b zz l

zc j zz l zz l

b(z)10

z, cm

r, cm

For p(z)=const, |W| is minimal for[Bushkova, Mirnov, Ryutov, 1986]

Rzz

BzB

m

111

)( 0

Optimal B(z) profile for GDT with p(z)=const

Magnetic field was originally optimized for p=const

0 50 100 150 200 250 300 350 4001

0

1

_rB2l 104

80 p_05_equali

5.3 103

P_rB2l

zz l zi zz l

More realistic p(z) profile

Now pressure is strongly anisotropic due to sloshing ions

z,cm

r''/rB2pr''/rB2 p

R=2, turning point for ions injected at 45

unfavorable curvature, r''<0

Magnetic field should be corrected to reduce unfavorable curvature. It will improve MHD stability.

Corrected coil positions in GDT

Minimization of potential energy W with p=p(B) for sloshing ions by shifting several coils reduces W by a factor of 2.7 compared to the present GDT system

Corrected coil positions in GDT

z,cm

GDT

pr''/rB2

pGDT

corrected

Relatively simple adjustment of coils can improve MHD stability

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

Increase of magnetic field

Additional coils from AMBAL-M with I=26.3 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 260<z<260 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

A.A. Ivanov “Perspectives of development of magnetic mirror traps in Novosibirsk”Friday, July 912:10

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