NSTX_U Design Point Studies

C Neumeyer5/4/6

1) Use of KCOOL to determine SS water cooled capacity…

a. TF inner leg J limitb. TF outer leg I limit

2) Plasma shape based on J Menard equilibrium

3) Scan of design points for t_flat ≥ 10s using…

a. LN2 (adiabatic 80K to 100C)b. Sub-cooling (adiabatic -50C to 100C) c. Water cooling (active cooling Tmax = 100C)

TF Inner Leg Water Cooling via KCOOL

Temperatures at 10 Locations along TF Inner Leg

0

20

40

60

80

100

120

0.00 5.00 10.00 15.00 20.00

Time (sec)

Temp (C)

TC1

TC2

TC3

TC4

TC5

TC6

TC7

TC8

TC9

TC10

Assumptions:1) 35% water fraction, 10% insulation fraction, 2 circular coolant passages per turn2) 10m/s limit on water flow velocity, 100C max T_cu3) No credit taken for counterflow option

Steady state:J_cu = 10.1kA/cm2

J_avg = 5.6 kA/cm2

Steady state:J_cu = 10.1kA/cm2

J_avg = 5.6 kA/cm2

TF Outer Leg Water Cooling via KCOOL

Assumptions:1) Existing conductor & cooling hole dimensions except tap added at midplane to create

two cooling circuits per outer leg2) 10m/s limit on water flow velocity, 100C max T_cu

Temperatures at 10 Locations along TF Outer Leg

0

20

40

60

80

100

120

0.00 20.00 40.00 60.00 80.00

Time (sec)

Temp (C)

TC1

TC2

TC3

TC4

TC5

TC6

TC7

TC8

TC9

TC10

Steady state: 121.5kAPulsed:Steady state: 121.5kAPulsed:

t (s) I_TF (A)10 18386320 14606530 13272840 12668150 12367760 122128

Plasma Shape

NSTX & NSTX-U Shapes

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

r(m)

z(m)

NSTX (95%) NSTX (100%)NSTX-U (95%)

NSTX-U (100%)

R0 0.854 0.854 0.903 0.903A 1.337 1.276 1.650 1.583a 0.639 0.669 0.547 0.571R0-a 0.215 0.185 0.356 0.333R0+a 1.493 1.523 1.451 1.474kappa 2.2 2.2 2.8 2.8delta 0.3 0.3 0.6 0.6Inboard midplane SOL 0.0307 0.0231Outboard midplane SOL 0.0307 0.0231

Assumptions:

1) Per J Menard, =2.8, =0.62) R0+a_100 =1.474m is 10cm inboard of HHFW antenna guards3) R0 = 0.903m

€

R(θ ) = R0 + a∗cos(θ +δ ∗sin(θ ))

€

Z(θ ) = κ ∗a∗sin(θ )

Seems a bit close based on simplified (non-divertor)shape model

Seems a bit close based on simplified (non-divertor)shape model

Constraints on Scans • Bt flat top for entire Ip≠0 duration• Ip_dot ramp-up = 5MA/s• Ip_dot ramp-down = 10MA/s

• Solenoid provides 100% of ramp-up flux based on Hirschman-Neilsonw/Li=0.5 and CE=0.25

• T_max OH & TF conductor = 100C•_max OH & TF conductor = 138MPA (20ksi)

• |I_oh| ≤ 24kA, V_oh=+/-8kV (2 anti-parallel strings of 8 PSS)• 36 turn TF coil• V_tf=+/-2kV (2 series x 6 parallel PSS)

Solutions optimized for maximum Ip

Note: Cases run with Ti=Te. However since they are limited by magnetics thereis minimal dependency on confinement model. This assumption was tested at high Ip cases.

Cases

Optimizer aims to maximize Ip in each case

Cooling Scheme Pulse Length Radial DimsLN2 to 80K then adiabatic during pulse 10,20,30,40,50,60s Optimized for 10s

LN2 to 80K then adiabatic during pulse 10,20,30,40,50,60sOptimized for each pulse length

Sub-cooled (ethylene glycol mixture) to -50C then adiabatic during pulse 10,20,30,40,50,60s Optimized for 10sSub-cooled (ethylene glycol mixture) to -50C then adiabatic during pulse 10,20,30,40,50,60s

Optimized for each pulse length

Steady state water cooled steady stateOptimized for steady state

1.000

1.500

2.000

2.500

3.000

3.500

4.000

0 10 20 30 40 50 60 70

Ip Flat Top (sec)

Ip (MA)

Ip[MA]_LN2Ip[MA]_LN2(10sd)Ip[MA]_SCIp[MA]_SC(10sd)Ip[MA]_SS

Ip vs. Pulse Length

Bt vs. Pulse Length

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

0 10 20 30 40 50 60 70

Ip Flat Top (sec)

Bt (T)

Bt[T]_LN2Bt[T]_LN2(10sd)Bt[T]_SCBt[T]_SC(10sd)Bt[T]_SSBt[T]_Oleg

Note: Outer Leg is not limitingNote: Outer Leg is not limiting

Solenoid Flux vs. Pulse Length

1.000

1.500

2.000

2.500

3.000

3.500

0 20 40 60

Ip Flat Top (sec)

Solenoid Flux (Volt-sec)

Flux_total_LN2Flux_total_LN2(10sd)Flux_total_SCFlux_total_SC(10sd)Flux_total_SS

Summary Comments

Results do not quite reach Ip and Bt levels from Masa’s strawman

Solenoid flux requirement may be less than assumed, need to compare formula used vs. experimental results

TF outer legs suit design points arrived at herein but need further enhancement in cooling (method TBD) to go higher in Bt

Need to look at outer PF coils long pulse and steady state limits

Design points arrived at herein are not strongly coupled to Ti=Te (or not) assumption, because magnetics is limiting and Paux=10MW appears tobe sufficient for supplemental NICD during flat top