Physics Analysis of FIRE

UFA 2nd Burning PlasmaWorkshop

May 1-3, 2001

General Atomics

S. C. JardinPPPL

with input from

C.Kessel, D.Meade, N.Gorelenkov, J.Manickam,J.Mandrekas, and the FIRE team

Outline

• Rational for the device design

• Nominal operating point and reference discharge

• Perturbation studies

• Heating, CD, and Fueling

• MHD stability and Energetic Particle Modes

• Device Flexibility and AT modes

• Sensitivity to Energy Confinement Time

• Summary

A simple systems power balance analysis providesa rational for optimizing the design point

Confinement (Elmy H-mode) ITER98(y,2):

τE = 0.144 I0.93 R1.39 a0.58 n200.41 B0.15 Ai

0.19 κ0.78 P heat -0.69 H(y,2)

Density Limit: n20 < 0.75 nGW = 0.75 IP/πa2

H-Mode Power Threshold: Pth > (2.84/Ai) n200.58 B0.82 R a0.81

MHD Stability: βN = β / (IP/aB) < 1.8

Engineering Constraints: 1. Flux swing requirements in OH coil (V-S)

2. Coil temperature not exceed 373o K

3. Coil stresses remain within allowables

Configuration Concept: 1. OH coils interior to TF coils, or

2. OH coils exterior to TF coils

βN = 1.5, qe = 3.13, Q=10, κ=1.8, Hy,2=1.0, τflat = 20 s

Aspect Ratio --- A

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2

Major R

adius -- R

2.0

2.5

3.0

3.5

4.0

B T=10 T

B T=9 T

B T=8 TB T=7TB

T=6 T

BT=5 T

BT=4 T

OH interior to TF Coil

OH exterior to TF Coil

FIRE

Major Radius required for power balance vs A

Aspect Ratio -- A

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2

Plasm

a Current I

P (M

A)

7

8

9

10

11

12

13

14

15

βN = 1.5, qe = 3.13, Q=10, κ=1.8, Hy,2=1, τflat = 20 s

BT = 10 T

BT = 9 T

BT = 8 T

BT = 7 T

B T = 6 T

B T = 5 T

B T = 4 T

OH interior to TF Coil

OH exterior to TF Coil FIRE

Plasma Current required for power balance vs A

10

85

1.3

BT = 0.30 T BT = 0.45 T

• TSC could reproduce the plasma current evolution using only the experimentalvalues of the PF current trajectories. Everything else is predictive

• Supported the correlation between the q=1 surface and termination of the current

TSC was used recently to model the NSTX current evolution for a ToroidalField scan series in order to establish the correlation between .

Red = data (EFIT)Black = TSC

Time (s)

0 5 10 15 20 25 30

Po

we

r (MW

) -10

0

10

20

30

40

50

Time (s)

0 5 10 15 20 25 30

Pla

sma

Cu

rren

t IP

(MA

)

0

2e+6

4e+6

6e+6

8e+6

R B

T (T

-m)

0

5

10

15

20

25

Total Power

alpha Power

ICRF Power

Ohmic Power

Radiation

TSC Simulation of Reference FIRE*Discharge with Burn Control

βP = 0.70 ne = 5 ×1020 τE = W/P = 800 ms = 0.8 H98(y,2) nα= 1019

βT = 2.1% Te0 = 11 keV = W/(P-PRAD) = 1100 ms = 1.1 H98(y,2) βα = 0.2%

βN = 1.6 % W = 32 MJ li (1)= 1.08 li (3)= 0.9

Why a 20 sec discharge ?

τE ~ 1 sec (energy confinement time)

Other timescales of interest:

• Current redistribution time ~ 10 s

• Burn control time ~ 5-10 s

• Helium Ash buildup time ~ 5-10

These transient phenomena and others beingstudied with TSC

Time (s)

0 5 10 15 20 25 30

Plasm

a Current

0

2e+6

4e+6

6e+6

8e+6

Total Plasma CurrentLHCD CurrentBootstrap CurrentTotal Noninductive Current

2D Graph 2

Time (s)

0 5 10 15 20 25 30 35

q=1 radius (m

)

0.0

0.1

0.2

0.3

0.4

l i(1)

0.8

1.0

1.2

1.4

1.6

q=1 radiusinternal inductance

• 1.75 MA LHCD turnedon at t=15 s

• requires over 10 sec forcurrent profile to adjust asseen by q=1 radius and li

TSC simulation of LHCD added to reference dischargeshows it takes 10-20 sec to equilibrate

Time (s)

0 5 10 15 20 25 30

ICR

F P

ower (M

W

0

5

10

15

20

25Time (s)

0 5 10 15 20 25 30

Helium

Density

0.0

5.0e+18

1.0e+19

1.5e+19

2.0e+19

2.5e+19

3.0e+19

3.5e+19

τP / τ

E = 5

τP/τE = 10

τP / τE = 50

τP / τ

E = 5

τP/τE = 10

τP / τE = 50

Comparison of 3 TSC FIRE simulations where τP ischanged suddenly at t=15 from 5τE to 10τE or 50τE

• natural equilibrationtime for helium ash is10-20 sec

• note, shows theimportance of particlecontrol in divertor

Power required tokeep stored energy at40 MJ

• Ion Cyclotron system

• Baseline system, heating only

• 30 MW to the plasma

• 100 – 150 MHz for 2ΩD ΩT , H or He3 minority

• High Frequency Fast Wave

• Optional /Partial replacement for ICRH

• Lower Hybrid System

• Possible upgrade

• 8 GHz , 2-ports for 25 MW total

Fire Heating and CD systems

2-strap ICRH antennain each of 4-ports

FIRE is considering both vertical and inside launch to allowdeep pellet penetration

• first 3D simulation of thisexperimentally discoveredphenomena was in M3D

[Strauss, Park, et al, Phys. Plasmas7 (2000) 250]

• led to development of 2Dmodel now in TSC code

[Jardin, Schmidt, et al, Nucl.Fusion 39 (2000) 923]

MHD Stability of Baseline Discharge

Baseline operating regime has very low βN (~1.5 to 2.0) andqe > 3.1, and therefore has good stability margins

However, there are areas requiring additional R&D:

• m=1 internal mode (monster sawtooth)

• Neoclassical tearing mode (NTM)

• Edge Localized Modes (ELMs)

• Energetic particle modes

• MHD stability limits for AT modes

Physics Question: Role of the m=1 mode

• FIRE will have a q=1 surface at 0.3 < r/a < 0.5 and will exhibit m=1(sawtooth)

• The question is when this mode couples to other modes and leads to a NTMor a disruption

• 3D Extended MHD simulation taking part as part of the SCIDAC initiativeare studying the m=1 mode in a burning plasma, taking into account:

• energetic particle drive,• kinetic stabilization,• 2-fluid effects, and• non-linear saturation mechanism

• This is one of the major thrusts of the 3D macroscopic simulationscommunities..similar to turbulent transport simulations in transport community

• LHCD can provide some control on this by decreasing the q=1 radius

High Field: 12 T, 7.7 MA

time (sec)

surf

ace

num

ber

edge

q = 1

q = 2

q = 3

PEST unstableeigenfunction att=12.5 sec

axis

Balloon and Mercier stability

r/a r/a

totaltotal

BSBS LHCD

q q

J|| J||

Radius of q=1 surface can be decreased by application of LHCD near edge

I(LHCD) r/a(q=1)

0.0 0.425

1.0 0.35

1.5 0.30

2.0 0.20

2.35 0.10

2.55 0.00

Critical βN fit for q=1 sawtoothed induced m/n=3/2 NTM

ν = νi/εωe*

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

ρi*

0.000

0.002

0.004

0.006

0.008

0.010

0.012

3.0

3.0

3.0

3.0

3.0

3.0

3.3

3.3

3.3

3.3

3.3

3.3

1.8

1.81.8

2.12.1

2.1

2.12.1

2.12.1

2.4

2.4

2.4

2.4

2.4

2.4

2.42.42.7

2.7

2.7

2.7

2.7

2.7

2.7

2.7

2.7

3.0

3.0

3.0

3.0

3.3

3.3

3.3

(From LaHaye, Butter, Guenter, Huysmans, Marashek, and Wilson)

Physicsquestion: NTM• neoclassical tearing mode setsβ limits in many long-pulsedischarges

• scaling of this to new deviceslargely result of empirical fittingof quasi-linear formula

• present scaling indicates thatFIRE will be stable to the NTMin the ignition regimes 1.5 < βN

< 1.8

• this is another major thrust of3D macroscopic modeling effort

• LHCD active feedback looksfeasible if needed (PHR)

Resonant TAEs are stable if βα0 < βα0crit = 0.66% => ne0 > 7.5 ×1020

Relaxed profiles are stable up to βα0crit =1%, ne0 > 6.3 ×1020

High-N non-perturbative Alfven modeStability Calculations (HINT)

FIRE Can Access Various Pulse Lengths byVarying BT

FIRE will have many features for AT operation

FIRE is Examining Ways to Feedback ControlRWM/Kink Modes

• Design willincorporate what islearned from DIII-Dand Columbiaexperiments

Identification of AT Targets for FIRE

• Long pulse AT modes are targeted to operate at reduced field (8.5T) forabout 40 sec ( > 3 Skin Times)

• We can project backwards from Standard Operating Modes to getrequirements on βN and H(y,2) for AT modes:

Stored Energy: W ~ βB2 ~ βNIB

Energy Confinent time: τE ~ H(y,2) IP.93 n.41 BT

.15

~ H(y,2) IP1.34 BT

.15

W ~ βB2 ~ βNIB

The operating pointson this graph willhave the same storedenergy for the βN

values shown on thecontours.

Q=5, BT=10,IP=6.44, H=1, βN=2.1 base case

No wall n=1 stab AT rule* need

3.1 3.4 2.7

3.5 3.7 3.2

*AT rule: lower of 4×li and 1.15 βN

q95

Q=5, BT=10,IP=6.44, H=1, βN=2.1 base case

The operating pointson this graph willhave the same energyconfinement timesfor the H(y,2) valuesshown on thecontours.

τE ~ H(y,2) IP.93 n.41 BT

.15

~ H(y,2)IP1.34 BT

.15

AT modes need H factor in range 1.2 –1.6 for same confinement time in sec.

FIRE’s Performance With Projected Confinement

FIRE Operating modes are within the Existing H-modeDatabase for both density and energy confinement

FIRE should be able to access AT Plasmas requiring bothhigh βN and high H(y,2)

MHD operating space for Tokamaks

εβP

0 .0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 .9 1.0

β/(Sε)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

βN=2

βN=3

βN=4

βN =5

q* = 2q* = 3

q* = 4

neoclassical tearing

n=1 RWM

6.5MA 10T, 18s,

7.7MA 10T, 18 s 150 MW

FIRE-AT1

FIRE

5.3 MA 8.5T, 35s 150 MW

FIRE*

Progress Toward ARIES-like Plasmas will Require a Sequence of Steps

q* = 3

n>1 RWM

q* = 4βN = 5

150 MW

q* = 2

ARIES-RS

ARIES-I

FIRE-AT0

εβP

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

β/(Sε)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

βN=2

βN=3

βN=4

βN=5

q* = 2q* = 3

q* = 4

neoclassical tearing

n=1 RWM

6.5MA10T, 18s,

7.7MA10T, 18 s150 MW

FIRE-AT1

FIRE

5.3 MA 8.5T, 35s 150 MW

FIRE*

q* = 3

n>1 RWM

q* = 4βN = 5

150 MW

q* = 2

ARIES-RS

ARIES-I

FIRE-AT0

FIRE can test advanced modes used in advanced reactor designs

Summary• There are no apparent physics showstoppers

• FIRE design is near optimal for Next-Step Mission

• FIRE will demonstrate and study high Q operation over abroad range of parameters for all relevant physics timescales

• High Q operation at low βN values down to ~1.5 greatlyincrease credibility of the device• There is great science to be learned. Eg., in the MHD area:

• How does core self-organize with α’s and m=1 mode?• How does edge self-organize with bootstrap and ELMs• Behavior of the neoclassical tearing mode at low ( ρ*,ν*)• How well can our codes predict these nonlinear events ?