Physics Analysis of FIRE UFA 2 nd Burning PlasmaWorkshop May 1-3, 2001 General Atomics S. C. Jardin PPPL with input from C.Kessel, D.Meade, N.Gorelenkov, J.Manickam, J.Mandrekas, and the FIRE team
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 ?