# Presentation: 574384

## 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 FIRE

- Plasma 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