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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

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Advanced tokamak plasmas and their control l.jpg

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 l.jpg
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 l.jpg
ARIES-AT Power Plant Design Provides a Goal for AT Research Tokamaks

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 westabilize n=1-4 with feedback? Do we need to?

IP/Ip=0.91, ICD=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 l.jpg

n=1 RWM feedback Tokamaks 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 currentfraction

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/nGreenwald ≈ 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 Physics Basis


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ARIES-AT Tokamaks

Layout


Next step devices must provide basis for tokamak power plant regime l.jpg
Next Step Devices Tokamaks Must Provide Basis for Tokamak Power Plant Regime

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

AT

KSTAR

FIRE

Inductive


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Objectives of FIRE Tokamaks

  • 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


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F Tokamaksusion Ignition Research Experiment


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FIRE’s Tokamaks 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


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0D Analysis Includes Tokamaks

  • 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


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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


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FIRE’s Q=5 AT Operating Space FIRE AT

Access to higher tflat/j decreases at higher N, higher Bt, and higher Q, since tflat 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 l.jpg
Observations from 0D Analysis for Burning Plasma AT FIRE 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

  • H98 ≥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


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FIRE’s AT Operating Space FIRE AT

Q = 5-10 accessible

N = 2.5-4.5 accessible

fbs = 50-90+ accessible

tflat/tj = 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/nGr = 0.6-1.0

n(0)/<n> = 1.5-2.0


Slide15 l.jpg

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

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


Dynamic simulations of fire at discharges with tsc lsc l.jpg
Dynamic Simulations of FIRE AT Discharges with TSC-LSC FIRE AT

  • 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


Slide17 l.jpg

Vertical position control coils FIRE AT

Passive stabilizers

TSC

Model


Tsc lsc simulation of q 5 fire at discharge l.jpg
TSC-LSC Simulation of FIRE ATQ≈5FIRE 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


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

During flattop, t=10-41s

li(3)=0.42



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MHD in FIRE AT Plasmas and its Control FIRE AT

  • 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 |’|


Slide22 l.jpg

Updating FIRE FIRE ATAT 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


Slide23 l.jpg

Stabilization of n=1 RWM is a FIRE ATHigh 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??


Stabilization of n 1 rwm on diii d l.jpg
Stabilization of n=1 RWM on DIII-D FIRE AT

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 l.jpg
Theoretical Results for n=1 RWM Stabilization from MARS and VALEN

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

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

HBT-EB


How do n 2 4 manifest themselves if they are linearly ideal unstable l.jpg
How Do n=2-4 Manifest Themselves if They Are Linearly Ideal Unstable

Shape study on DIII-D AT plasmas

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

wall at 1.5a


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Neo-Classical Tearing Modes Unstable for FIRE AT Modes

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 avoid NTM’s with j() and q>2.0

or do we need to suppress them??

Ro

Ro+a

Bt=6.5 T

fce=182

fce=142

170 GHz

Ro

Ro+a

Bt=7.5 T

fce=210

fce=164

200 GHz

Ro

Ro+a

Bt=8.5 T

fce=238

fce=190

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


Slide29 l.jpg

J. Decker, APS 2002,MIT Unstable

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


Slide30 l.jpg

Comments on ECCD in FIRE Unstable

  • 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


Slide31 l.jpg

FIRE EC Geometry Unstable

ce = 

n(0)=4.51020

f pe=9√n

Rays are bent as they  approaches pe

EC launcher

Rays must be launched with toroidal directionality for CD

pe > 

cutofffor 170 GHz


Neo classical tearing mode stabilization on diii d asdex u and jt 60u l.jpg
Neo-Classical Tearing Mode Stabilization on DIII-D, ASDEX-U and JT-60U

  • Actively stabilize NTM’s ---> must spatially track island

    • ECCD

    • LHCD (Compass-D)

  • Passively avoid NTM’s

    • q > 2?

    • J() that is stable?

DIII-D

Required IECCD scales as Ip and N2

ASDEX-U


Heating and current drive for fire at plasmas and its control l.jpg
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 l.jpg
ICRF Ion Heating Control

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


Slide35 l.jpg

ICRF/FW Viable for FIRE On-Axis CD Control

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)

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??

E. Jaeger, ORNL


Slide36 l.jpg

Benchmarks for LHCD Between LSC and ACCOME (Bonoli) Control

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 l.jpg
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 shearand 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



Glf23 at predictive modeling is improving l.jpg
GLF23 AT Predictive Modeling Is Improving Mechanisms

Kinsey

Ti, Te

V

GLF23, ver. 1.61

model

DIII-D

expt



Slide41 l.jpg

HFS Launch Mechanisms

V=125 m/s, set by ORNL pellet tube geometry

Vertical and LFS launch access higher velocities


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HFS Pellet Launch and Density Peaking ---> MechanismsNeeds Strong Pumping

Simulation by W. Houlberg, ORNL, WHIST

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

P. T. Lang, J. Nuc. Mater., 2001, on ASDEX and JET

L. R. Baylor, Phys. Plasmas, 2000, on DIII-D



Slide44 l.jpg

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

D. Dreimeyer, M. Ulrickson


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Other Issues for FIRE AT Plasmas Mechanisms

  • 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


Slide46 l.jpg

TF Ripple and Alpha Particle Losses Mechanisms

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


Slide47 l.jpg

Fe Shims for Ripple Reduction for AT Modes in FIRE Mechanisms

TF Coil

Fe Shims

Outer VV

Inner VV


Slide48 l.jpg

PF Coil Mechanisms Capability for AT Modes

AT modes have flattops ranging from 16-50 s

  • 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


Slide49 l.jpg

AT Physics Capability on FIRE Mechanisms

Control

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

MHD

J Profile

P-profile

Rotation


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Ongoing Work to Establish Advanced Tokamak Regime for FIRE Mechanisms

  • 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


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