Advanced Tokamak Modeling for FIRE

C. Kessel, PPPL

NSO/PAC Meeting, University of Wisconsin, July 10-11, 2001

Systems Analysis of Burning AT Plasmas in FIRE

• Using the FIRE baseline (R=2.0 m, A=3.8) solutions are found which satisfy:– Power balance with Q=10– PCD < Paux = 5Palpha/Q, CD = 0.45 A/W-m2 from CD calculations– Pfusion < 250 MW, Palpha < 50 MW

• While varying – BT (6.5 - 9.5 T)– q95 (3.1-4.7)– n(0)/<n> (1.25-2.0)– N (2.5-4.5)– n/nGr (0.45-0.85)

Applying Constraints Shows Viable Q=10 Burning AT Plasmas Exist

System Analysis Is Searching for Lowest H98 Factors for AT Plasmas

Each N has a best (Bt, q95) combination to get lowest H98

N = 2.5; Bt=9.5, q95=4.3

N = 3.0; Bt=8.5, q95=3.7

N = 3.5; Bt=7.5, q95=3.5

Highest n(0)/<n> leads to lowest H98

Highest allowed n/nGr leads to lowest H98

Quasi-Stationary AT Burning Plasmas are the Primary Focus

• Plasma current is ramped up with inductive and non-inductive current to produce a quasi-stationary plasma at the beginning of flattop

• The safety factor is held by non-inductive current– Bootstrap current– LHCD off-axis– ICRF/FW on axis

• Flattop times 2-4 x jdiff (30-60 s)• Q=5-10• 1.0 < H(y,2) < 1.8

transient burning AT plasmas can be produced with inductive current

long pulse DD (non-burning) plasmas can be created with pulse lengths up to >200 s at Bt=4 T, Ip=2 MA

FIRE Can Access Various Pulse Lengths by Varying BT

Ideal MHD Stability and LHCD Analysis Identifies an AT Plasma Target

• No n=1 stabilization– N = 2.5– fbs < 0.55

• With n=1 stabilization– N = 3.6– fbs < 0.75

*plasmas with qmin = 1.3-1.4 also identified, but these have (3,2) and (2,1) NTMs, and no improvement in N when n=1 is stabilized (for feedback approach, not rotation method)

**pockets of n=1 stability at qmin just above integer values are found, although the depth of the pocket is unclear

***LHCD calculations show that waves can not penetrate inside of r/a = 0.5-0.6 for typical plasma parameters

q(min) = 2.1-2.2, r/a(min) = 0.8, Ip(MA) < 5.5, Bt(T) = 8.5

Benefit of n=1 RWM Stabilization

n=1 stabilized

N = 3.6

fbs = 0.75

ILH = 1.4 MA

IBS = 3.8 MA

n=1 not stabilized

N = 2.55

fbs = 0.55

ILH = 2.2 MA

IBS = 3.0 MA

qmin = 2.1, r/a(qmin) = 0.8, Ip = 5.3 MA, BT = 8.5 T, R/a = 3.8, (5,2) and (3,1) NTM’s, allows wider range for value of qmin, n(0)/<n> = 1.5

LHCD shape and location approximation from ray-tracing calculations

Rotation or Feedback Coil for n=1 External Kink Mode (RWM) Stabilization on FIRE

• Plasma rotation theory– Require rotation of 1-10% of

Alfven speed– Conducting shell located

inside the critical ideal wall and outside the critical resistive wall*

– Dissipation mechanism in plasma

– Error field control (DIII-D experience)

• Feedback control theory– Require feedback coils to

produce field with given toroidal mode number (n=1)

– Conducting shell to slow instability growth time to feedback timescales*

– Field sensors preferably between conducting shell and plasma

*for rotation detailed wall geometry is important, for feedback it is not

FIRE is Examining Ways to Feedback Control RWM/Kink Modes

Feedback Coils:

n=2 sets limit N=3.6

Rotation: (NBI)

continuous wall on outboard side, n=1 N>4.5, with n=2,3 setting the limit

model partial wall on outboard side, n=1 N=3.45, n=2 limit??

Is rotation better or worse than feedback coils with a realistic partial wall?

External Current Drive and Heating for FIRE

• 30 MW ICRF (ion heating) for ELMy H-mode;– 4 ports, 100-150 MHz

• <10 MW ICRF/FW (electron heating/CD) for AT mode;– 1 (or 2) ports, 90-110 MHz,

phasable– Want to use same ICRF

equipment

• 20 MW LHCD (electron heating/CD) for AT mode;– 2-3 ports, 5.6 GHz, n||

=2.0-2.5– For NTM control

• ?? MW ECH/ECCD (electron heating/CD) for startup

RFCD Analysis for FIRE Burning AT Plasmas

• ICRF/FW (T.K. Mau)• ne(0) = 3.4 x 10^20• Te(0) = 20 keV• Zeff = 1.4, N = 2.55,

Bt = 8.5 T– = 100 MHz– n|| = 2.0– PFW = 3.6 MW– IFW = 0.30 MA

• LHCD (LSC code) • ne(0) = 4.5 x 10^20• n(0)/<n> = 1.5• Te(0) = 22 keV• Zeff = 1.45, N = 3.5,

Bt = 8.5 T– = 5.6 GHz– n|| = 2.0, n|| = 0.3– PLH = 20 MW– ILH = 1.7 MA

CD efficiencies and deposition depend on details of n and T profiles

LHCD Calculation for FIRE with LSC Ray-Tracing Code

PLH = 17.5 MW

ILH = 1.65 MA

n|| = 1.90, n|| = 0.3, = 5.6 GHz

IBS = 3.8 MA, Ip = 5.5 MA

N = 3.8, ne(0) = 4.6 x 10^20

n(0)/<n> = 1.4

Dynamic Burning AT Simulations with TSC-LSC for FIRE

Ip=5.5 MA, Bt=8.5 T, Q=7.5, N=3.0, =4.4%, PLH=20 MW, ILH=1.7 MA, IBS=3.5 MA, IFW=0.35 MA

H(y,2)=1.6

Dynamic Burning AT Simulations with TSC-LSC for FIREPlasma becomes quasi-stationary after 10 s

Future Work for FIRE Burning AT Plasma Development

• Target AT plasmas found by systems study

• Continue ideal MHD stability search– Pressure profile and q*

variations– Edge profile effects– n=1 stabilized plasmas

• NTM requirements• Examine DIII-D AT experiments• Examine C-Mod AT experiments

• CD analysis– Reduce PCD, raise fbs– LHCD, HHFW, NBI– ICRF/FW– ECH/ECCD

• TSC-LSC dynamic discharge simulations– Plasma formation in shortest

time– Energy and particle transport

models– Control of j, n, T

Conclusions• Systems analysis shows range of Q=10 burning AT plasmas with H98 > 1.4• qmin around 2.1-2.2 is found to provide a good combination of

– Beta limit with and without n=1 stabilization--increase these– High plasma current--not too high– Elimination of (3,2) and (2,1) NTM’s--but (5,2) and (3,1) exist– Lower CD power --need to reduce this

• Less than 2 MA of LHCD is required, leading to powers of 20 MW from LSC lower hybrid calculations

• Stabilization of n=1 RWM would yeild attractive configuratons; rotation versus feedback coils?

• Need to find techniques for density profile peaking to enhance bootstrap current and reduce LHCD power

• TSC-LSC simulations indicate that we can create quasi-stationary plasmas for flattop burn