# Presentation: 170361

## Advanced Tokamak Plasmas and Their Control

- C. Kessel
- Princeton Plasma Physics Laboratory
- Columbia University, 4/4/03

## Power Plant Studies Show the Potential Benefits of Advanced Tokamaks

- Simultaneous achievement of
- Steady state
- High  ----> high fusion power density
- Large bootstrap (self-driven) current ----> low recirculating power
- Good energy confinement consistent with the high  and high fBS ----> high fusion gain
- This combination drives down the machine size and cost of electricity (COE)
- High potential benefits of Advanced Tokamak operation make AT research on any Burning Plasma Experiment mandatory (Snowmass 1999)
- Present tokamak experiments pursuing AT plasma physics worldwide

## ARIES-AT Power Plant Design Provides a Goal for AT Research

- Ip=12.8 MA, BT=5.9 T, R=5.20 m, a=1.30 m, X=2.20, X=0.9

******N****=5.4** **--->** **can we** **stabilize n=1-4 with feedback? Do we need to?**
**I********P****/Ip=0.91, I****CD****=1.25 MA**
**---> can the current profile be dominated by bootstrap current, and can it be controlled?**
**Pressure profile optimized** to maximize N, and T and n chosen to maximize bootstrap current with ITB in location of qmin **---> can transport be controlled to provide this?**
**Plasma edge** must be consistent with the divertor, CD, power handling **---> what can be produced and controlled? **

## ARIES-AT Physics Basis

**n=1 RWM feedback**** control with coils: do we need to stabilize n>1? Use higher order coils for higher n **
**No plasma rotation**** source**
**37 MW ****LHCD ****and  5 MW (25 MW capable) ****ICRF/FW**** for external current drive/heating**
**HHFW and NBI (120 keV) also shown capable of providing CD **
**NTM**** stability: are (5,2) and (3,1) unstable? LH current profile modification (********’) at (5,2)**
**90%bootstrap current**** ****fraction**
**Strong plasma shaping**
**Double null**
**Tungsten divertors allow high heat flux**

**Vertical and kink passive stability: tungsten**** structures in blanket, feedback coils behind shield**
**Transport**** assumed roughly agreed with ****GLF23****: new versions of GLF23 are now available**
**Very low ripple (0.02%)**
**n/n****Greenwald**** ≈ 1**
**Plasma edge and divertor solution: balancing of ****radiating mantle and radiating divertor,**** with Ar impurity**
**High field side pellet**** launch allows fueling to core, and ********P*********/********E****=10**** allows sufficiently low dilution**

## ARIES-AT

**ARIES-AT**
**Layout**

## Next Step Devices Must Provide Basis for Tokamak Power Plant Regime

**FIRE**

**Inductive**

**AT**

**KSTAR**

**ITER, KSTAR, JT-60U have super-conducting coils**
**ITER is DT**
**Shielding required**
**JT-60SC and KSTAR are DD**

**FIRE has Cu coils**
**FIRE is DT**
**Minimal shielding**

## Objectives of FIRE

- Develop the experimental/theoretical basis for burning plasma physics
- Q ≈ 10 ELMy H-mode for burn > 2  cr
- Q ≥ 5 Advanced Tokamak for burn > 1-5  cr
- Adopt as many features as possible of projected Power Plant designs
- Only address technological issues required for successful device operation
- Fueling, pumping, power handling, plasma control, neutronics, materials, remote handling, and safety
- Utilize the compact high-field Cu coil approach_ to keep the device cost at ≈ $1 B_

## Fusion Ignition Research Experiment

## FIRE’s Efforts to Self-Consistently Simulate Advanced Tokamak Modes

_**0-D Systems Analysis**_**:**
- Determine viable operating point global parameters that satisfy constraints
_**Plasma Equilibrium and Ideal MHD Stability**_:
- Determine self-consistent stable plasma configurations to serve as targets
_**Heating/Current Drive**_:
- Determine current drive efficiencies and deposition profiles
_**Transport**_**:(GLF23 and pellet fueling models to be used in TSC)**
- Determine plasma density and temperature profiles consistent with heating/fueling and plasma confinement
_**Dynamic Evolution Simulations**_:
- Demonstrate self-consistent startup/formation and control including transport, current drive, and equilibrium
_**Edge/SOL/Divertor**_**:**
- Find self-consistent solutions connecting the core plasma with the divertor

## 0D Analysis Includes

- Power balance: energy confinement time scaling
- Fusion cross-section from Bosch-Hale formulation
- Particle balance: self-consistent helium content (input He*/E), quasi-neutrality, input impurity fractions
- Radiation: bremsstrahlung, cyclotron (new Albajar formulation), line (coronal equilibrium)
- Current diffusion time, flux consumption (Hirshman-Nielson) with neoclassical resistivity
- Bootstrap current (equilibrium fits) and external CD: input CD efficiency
- Fast alpha beta contribution
- Parabolic or parabolic+pedestal profiles
- Post-processor used for database screening

## 0D Power/Particle Balance Identifies Operating Space for FIRE AT

- Heating/CD Powers
- ICRF/FW, 30 MW
- LHCD, 30 MW
- Using CD efficiencies
- (FW)=0.20 A/W-m2
- (LH)=0.16 A/W-m2
- P(FW) and P(LH) determined at r/a=0 and r/a=0.75
- I(FW)=0.2 MA
- I(LH)=Ip(1-fbs)
- Scanning Bt, q95, n(0)/<n>, T(0)/<T>, n/nGr, N, fBe, fAr

- Q=5
- Constraints:
- (flattop)/(CR) determined by VV nuclear heat (4875 MW-s) or TF coil (20s at 10T, 50s at 6.5T)
- P(LH) and P(FW) ≤ max installed powers
- P(LH)+P(FW) ≤ Paux
- Q(first wall) < 1.0 MW/m2 with peaking of 2.0
- P(SOL)-Pdiv(rad) < 28 MW
- Qdiv(rad) < 8 MW/m2

**Generate large database and then screen for viable points**

## FIRE’s Q=5 AT Operating Space

**Access to higher t****flat****/********j**** decreases at higher ********N, higher Bt, and higher Q, since t****flat**** is set by VV nuclear heating**
**Access to higher radiated power fractions in the divertor enlarges operating space significantly**

## Observations from 0D Analysis for Burning Plasma AT

- In order to provide reasonable fusion gain Q≥5, _can’t operate at low density_ to maximize CD efficiency
- _Density profile peaking is beneficial_ (pellets or ITB), since broad densities increase required H98 and PCD
- Access to _high density_ relative to Greenwald density, in combination with _high bootstrap_ current fraction gives the lowest required H98
- _H__98 __≥1.4 are required to access ____flattop__/____curr diff __> 3_, however, the ELMy H-mode scaling law is known to have a  degradation that is not observed on individual experiments
- _Radiative core/divertor solutions_ are a critical area for the viability of burning AT experiments due to high P+PCD, suggesting impurity control techniques

## FIRE’s AT Operating Space

**Q = 5-10 accessible**
******N**** = 2.5-4.5 accessible**
**f****bs**** = 50-90+ accessible**
**t****flat****/t****j**** = 1-5 accessible**
**If we can access.....**
**H98(y,2) = 1.2-2.0**
**Pdiv(rad) = 0.5-1.0 P(SOL)**
**Zeff = 1.5-2.3**
**n/n****Gr**** = 0.6-1.0**
**n(0)/<n> = 1.5-2.0**

## Examples of Q=5 AT Points That Obtain flat/J > 3

| n | n | T | T | BT | q95 | Ip | HH | fGr | fBS | Pcd | P | zeff | fBe | fAr | t/ |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 0.5 | 2.60 | 1.5 | 8.17 | 6.5 | 4.25 | 4.25 | 1.71 | 0.8 | 0.80 | 27.5 | 27.8 | 2.08 | 1% | .3% | 3.58 |
| 0.5 | 2.93 | 2.0 | 7.28 | 6.5 | 4.25 | 4.25 | 1.57 | 0.9 | 0.80 | 30.9 | 31.4 | 1.77 | 1% | .2% | 3.95 |
| 0.75 | 3.10 | 1.5 | 7.83 | 6.5 | 3.75 | 4.82 | 1.46 | 0.9 | 0.80 | 33.1 | 36.5 | 1.89 | 2% | .2% | 3.07 |
| 0.75 | 2.91 | 1.0 | 7.71 | 6.5 | 4.00 | 4.52 | 1.62 | 0.9 | 0.85 | 24.7 | 28.6 | 1.77 | 1% | .2% | 3.52 |
| 0.75 | 3.23 | 1.5 | 7.00 | 6.5 | 4.00 | 4.52 | 1.54 | 1.0 | 0.85 | 27.5 | 32.0 | 2.08 | 1% | .3% | 4.40 |
| 0.75 | 2.44 | 1.5 | 8.90 | 6.5 | 4.25 | 4.25 | 1.74 | 0.8 | 0.91 | 16.0 | 28.0 | 2.20 | 2% | .3% | 3.65 |
| 1.00 | 3.49 | 1.0 | 7.35 | 6.5 | 3.50 | 5.16 | 1.36 | 1.0 | 0.83 | 32.6 | 38.6 | 1.77 | 1% | .2% | 3.00 |
| 1.00 | 3.26 | 1.0 | 7.60 | 6.5 | 3.75 | 4.82 | 1.54 | 1.0 | 0.89 | 23.9 | 30.1 | 2.01 | 3% | .2% | 4.00 |
| 1.00 | 2.44 | 1.5 | 9.59 | 6.5 | 4.00 | 4.52 | 1.65 | 0.8 | 0.95 | 13.6 | 31.5 | 2.32 | 3% | .3% | 3.29 |

- HH < 1.75, satisfy all power constraints, Pdiv(rad) < 0.5 P(SOL)

## Dynamic Simulations of FIRE AT Discharges with TSC-LSC

- Free-boundary time-dependent simulation 2D MHD equations, Maxwell’s equations, and 1D transport equations for particles, energy, and current, coupled thru boundary conditions to the PF coils
- Physics models
- Transport coefficients
- Heating/fueling deposition for alphas, NBI, ICRF, etc.
- Current drive and bootstrap current
- Sawteeth
- Radiation
- Impurity transport
- Feedback control systems
- High-n ballooning
- LSC is a lower hybrid ray-tracing code

## TSC

_**TSC**_
_**Model**_

## TSC-LSC Simulation of Q≈5 FIRE AT Discharge

- Ip = 4.5 MA, Bt = 6.5 T, N = 4.1,
- H98=1.7, n/nGr= 0.85, n(0)/n = 1.45
-  = 4.7%, p = 2.35, flattop/curr diff = 3.5,
- Zeff = 2.2, q(0) = 4.0, qmin = 2.7, q95 = 4.0

## TSC-LSC Simulation of Q=5 AT Burning Plasma

- During flattop, t=10-41s

- li(3)=0.42

## TSC-LSC Simulation of Q=5 AT Burning Plasma

## MHD in FIRE AT Plasmas and its Control 

_**n=∞ ballooning modes**_  ---> limit pressure locally, not observed experimentally since very localized, self-limiting by adjusting profile to be marginally stable
_**n=0 vertical instability**_  ---> slowed with conducting structures and controlled with coils that provide a radial magnetic field
_**n=1 external kink modes (resistive wall modes)**_ ---> disruptive, slowed with conducting structures and can be controlled with plasma rotation and/or direct feedback with saddle coils, strong influence of error fields
_**1 < n < 4 external kink modes --->  disruptive**_??, behavior similar to n=1, however, more localized toward the plasma boundary, and may set lower -limit than n=1, should be controllable like n=1 if necessary
_**4 < n < 20 peeling modes**_ ---> ballooning and kink mode character, localized to the plasma edge, associated with pressure pedestal and associated bootstrap current, and considered primary candidate for ELMs, plasma shaping has significant influence
_**Neo-classical tearing modes**_  ---> non-disruptive but reduce achievable  in long pulse discharges, controllable with current driven at island or by modifying current profile to increase |’|

## Updating FIRE AT Equilibrium Targets Based on TSC-LSC Equilibrium

**TSC-LSC equilibrium**
- Ip=4.5 MA
- Bt=6.5 T
- q(0)=3.5, qmin=2.8
- N=4.2, =4.9%, p=2.3
- li(1)=0.55, li(3)=0.42
- p(0)/p=2.45
- n(0)/n=1.4
- Stable n=
- Stable n=1,2,3 with no wall

- √V/Vo

## Stabilization of n=1 RWM is a High Priority on FIRE

- Feedback stabilization analysis with VALEN shows strong improvement in , _taking advantage of __DIII-D__ experience, _most recent analysis indicates N(n=1) can reach 4.2_ _

_**What is impact of n=2??**_

## Slide 24

## Stabilization of n=1 RWM on DIII-D

- Experiments on **DIII-D** have **verified plasma rotation stabilization** by reducing the error fields (amplified by RWM’s) that slow the plasma down, and **VALEN analysis** shows that better sensors and in-vessel feedback coils strongly improve N

## Theoretical Results for n=1 RWM Stabilization from MARS and VALEN

- MARS shows that feedback can work with simple structure and coil model

- VALEN shows that feedback can work with detailed structure and coil model

**HBT-EB**

## How Do n=2-4 Manifest Themselves if They Are Linearly Ideal Unstable

- _n=2 and n=3 would not allow access to the n=1 ____-limit_
- These modes appear too broad to be peeling modes
- This feature is common from wall stabilized ideal MHD analysis
**Are these modes triggering tearing modes that subsequently become NTM’s?? ---> DIII-D**

- Shape study on DIII-D AT plasmas

- wall at 1.5a

## Neo-Classical Tearing Modes for FIRE AT Modes

- Bt=6.5 T

- Bt=7.5 T

- Bt=8.5 T

- Ro

- Ro

- Ro

- Ro+a

- Ro+a

- Ro+a

- fce=182

- fce=142

- fce=210

- fce=164

- fce=190

- fce=238

- 

- 

- 

- 

- 170 GHz

- 200 GHz

- _Target Bt=6.5-7 T for NTM control_, to utilize 170 GHz from ITER R&D
- _Must remain on LFS for resonance and use O-mode, due to high Bt_
- ECCD efficiency?? (trapping)

_**Can we rely on OKCD to suppress NTM’s far off-axis on LFS versus ECCD ?? (enhanced Ohkawa affect at plasma edge)**_

- Can we avoid NTM’s with j() and q>2.0
- or do we need to suppress them??

## J. Decker, APS 2002,MIT

**OKCD allows LFS EC deposition, with similar A/W as ECCD on HFS **

## Comments on ECCD in FIRE

- ASDEX-U shows that 3/2 island is suppressed for about 1 MW of power with IECCD/Ip = 1.6%, giving 0.013 A/W
- Ip=0.8 MA and N=2.5
- DIII-D shows that 3/2 island is suppressed for about 1.2-1.8 MW with jEC/jBS = 1.2-2.0
- Ip=1.0-1.2 MA, N=2.0-2.5
- OKCD analysis of Alcator-CMOD gives about 0.0056 A/W
- FIRE’s current requirement should be about 15 times higher than ASDEX-U (scaled by Ip and N2)
- Need about 200 kA, which would require about 35 MW?? Early detection reduces power alot according to ITER
- Do we need less current for 5/2 or 3/1, do we need to suppress them??
- Is 170 GHz really the cliff in EC technology??

- MIT, short pulse results

## FIRE EC Geometry

******pe**** > ******
**cutoff** **for 170 GHz**

**EC launcher**

******ce**** = ******

- _FIRE EC Geometry_

- Rays are bent as they  approaches pe

- Rays must be launched with toroidal directionality for CD

- n(0)=4.51020
- f pe=9√n

## Neo-Classical Tearing Mode Stabilization on DIII-D, ASDEX-U and JT-60U

**ASDEX-U**

**DIII-D**

**Actively stabilize NTM’s** ---> must spatially track island
- ECCD
- LHCD (Compass-D)
**Passively avoid NTM’s**
- q > 2?
- J() that is stable?

**Required I****ECCD**** scales as Ip and ********N****2**

## Heating and Current Drive for FIRE AT Plasmas and its Control

- ICRF ion heating on and off-axis
- ICRF/FW for electron heating and on-axis CD
- LH for off-axis CD and electron heating
- EC for NTM control off-axis deposition _(no analysis yet_)
- NBI?? presently being examined (_no AT analysis yet_)
- High energy needed for ELMy H-mode, not practical
- AT’s have slightly lower density, more density peaking, and off-axis deposition is desirable ---> prefer conventional energies 120 keV
**Heating and Current Drive directly affect Transport**

## ICRF Ion Heating

**80-120 MHz**, 2 strap antennas, 4 ports, **20 MW** (10 MW upgrade)
- He3 minority, 2T, 2D, H minority accessible resonances at center and off-axis (C-Mod ITB) ----> full wave analysis gives 75% power on ions

## ICRF/FW Viable for FIRE On-Axis CD

- _PICES (ORNL) and CURRAY(UCSD) analysis _
- f = 110-115 MHz
- n|| = 2.0
- n(0) = 5x10^20 /m3
- T(0) = 14 keV
- 40% power in good part of spectrum (2 strap)
- ---->  0.02-0.03 A/W
- CD efficiency with 4 strap antennas is 50% higher
- Operating at lower frequency to avoid ion resonances, vph/vth??

- Calculations assume same ICRF ion heating system frequency range, approximately 40% of power absorbed on ions, can provide required AT on-axis current of 0.3-0.4 MA with 20 MW (2 strap antennas)

- E. Jaeger, ORNL

## Benchmarks for LHCD Between LSC and ACCOME (Bonoli)

- Trapped electron effects reduce CD efficiency
- Reverse power/current reduces forward CD
- Less than 1.0 MW is absorbed by alphas
- Recent modeling with CQL and ACCOME/LH19 will improve CD efficiency, but right now........
- Bt=8.5T ----> 0.25 A/W-m2
- Bt=6.5T ----> 0.16 A/W-m2
_**FIRE has increased the LH power from 20 to 30 MW**_

- f=4.6 GHz
- n ||=2.0
- n||=0.3

## Energy and Particle Transport in FIRE AT Plasmas and Its Control 

- Significant reductions in particle and energy transport have been achieved at the _plasma edge (ETB) and in the core (ITB)_
- Most present tokamaks have _NBI,_ which provides _sheared rotation_ and strongly stabilizes micro-instabilities
- _Negative magnetic shear_ _and Shafranov shift_ are also found to stabilize microinstabilites
**Heating, current drive, rotation, pellets, and impurities are found to influence transport**
- It appears that transport barriers can be made to _“leak a little” to avoid excessive particle buildup_
- Lots of other observations ---> C-Mod ITB’s with off-axis ICRF, JET ITB’s triggered by qmin passing rational surfaces,...
**The control of transport (pressure profile control) is critical to achieving high bootstrap current fractions, that remain MHD stable**
**The transport barrier may be an ideal method for controlling the pressure profile ---> by turning the ITB on and off, with a given frequency, a desirable pressure profile could be produced**

## Transport Has Multiple Scales and Multiple Stabilization Mechanisms

## GLF23 AT Predictive Modeling Is Improving

- Kinsey

- Ti, Te

- V

- GLF23, ver. 1.61

- model

- expt

**DIII-D**

## FIRE Pellet Launch Geometry

## HFS Launch

**HFS Launch**
**V=125 m/s, set by ORNL pellet tube geometry**
**Vertical and LFS launch access higher velocities **

## HFS Pellet Launch and Density Peaking ---> Needs Strong Pumping

- FIRE reference discharge with uniform pellet deposition, achieves n(0)/<n> ≈ 1.25

- Simulation by W. Houlberg, ORNL, WHIST

- P. T. Lang, J. Nuc. Mater., 2001, on ASDEX and JET
- L. R. Baylor, Phys. Plasmas, 2000, on DIII-D

## FIRE Uses Cryo-Pumping Coupled to Turbopumps

## FIRE’s Divertor Must Handle Attached(25 MW/m2) and Detached(5 MW/m2) Operation

- D. Dreimeyer, M. Ulrickson

## Other Issues for FIRE AT Plasmas

- Alpha particle losses from ripple, aggravated by high safety factor and low Ip and Bt
- TAE’s are also driven more easily at high safety factor (_not analized)_
- PF Coil operational flexibility for AT modes in FIRE

## TF Ripple and Alpha Particle Losses

- _TF ripple very low in FIRE_
- (max) = 0.3% (outboard midplane)
- Alpha particle collisionless + collisional losses = 0.3% for reference ELMy H-mode
- For AT plasmas alpha losses range from 2-8% depending on Ip and Bt
- ----> are Fe inserts required for AT operation??? _Optimize for Bt=6.5T_

## Fe Shims for Ripple Reduction for AT Modes in FIRE

**TF Coil**

**Outer VV**

**Inner VV**

**Fe Shims**

## PF Coil Capability for AT Modes

- Advanced tokamak plasmas
- Range of current profiles: 0.35 < li(3) < 0.55
- Range of pressures: 2.50 < N < 5.0
- Range of flattop flux states: chosen to minimize heating and depends on flattop time (determined by Pfusion)
- Ip limited to ≤ 5.5 MA
- _Lower li operating space led to redesign of divertor coils_
- PF1 and PF2 changed to 3 coils and total cross-section enlarged
- Presently examining magnet stresses and heating for AT scenarios

- AT modes have flattops ranging from 16-50 s

## AT Physics Capability on FIRE

- Strong plasma shaping and control
- Pellet injection, divertor pumping, impurity injection
- FWCD (electron heating/CD) on-axis, ICRF ion heating on/off-axis
- LHCD (electron heating/CD) off-axis
**ECCD (LFS, electron heating) off-axis, MHD control**
- RWM MHD feedback control
**NBI ?? (need to examine for AT parameters!!)**
- t(flattop)/t(curr diff) = 1-5
**Diagnostics**

_**Control**_

- MHD
- J Profile
- P-profile
- Rotation

## Ongoing Work to Establish Advanced Tokamak Regime for FIRE

- Establish PF Coil operating limits
- Revisit Equilibrium/Stability Analysis
- _Use recent GLF23 update in AT scenarios_
- LHCD efficiency updates
- EC with FIRE’s parameters
- Orbit calculations of lost alphas for scenario plasmas, Fe shim requirements
- RWM coil design in port plugs and RF ports
- Determine possible impact of n=2 RWM on access to high N
- Examine NBI for FIRE AT parameters