International Spherical Tori Workshop 2009, Madison, WI1 Modelling plasma scenarios for MAST-Upgrade Neutral beam requirements, sensitivity studies and

International Spherical Tori Workshop 2009, Madison, WI 1

Modelling plasma scenarios for MAST-Upgrade Neutral beam requirements, sensitivity studies and

stability

D. Keeling R. Akers , I. Chapman, G. Cunningham, H. Meyer, S. Pinches, S. Saarelma,

O. Zolotukhin and the MAST team

EURATOM/UKAEA Fusion AssociationCulham Centre for Fusion Energy

Culham Science Centre,

Abingdon, Oxon, OX14 3DB, UK.


Outline

• Overview of the MAST-U project• Baseline scenarios modelling methodology• Scenario sensitivity studies

– Example 1 - PINI position and tangency radius

– Example 2 - Te/ne profiles

• ASTRA studies• MHD stability studies


MAST Upgrade principal features

• Long pulse (t ~ 5 R), fully non-inductive to prove current drive physics on and off-axis.


• High Bt and off-axis NBI (5 MW) to access q(r) > 2 avoiding low n MHD test CTF-like q(r).


• Cryo pumped closed divertor density control

• Cryo pumped closed divertor density control

• EBW (~ 1 MW) to test heating and current drive and start-up


• On axis co- and counter current NBI (each 2.5 MW) for q-profile control, rotation and fast particle physics


Closed divertorClosed divertor

More flux, higher TFMore flux, higher TF

Cryo-pumpsCryo-pumps

12.5 MW NBI12.5 MW NBI


MAST Upgrade principal features









• Advanced divertor concepts can be tested DEMO, ST

• Advanced divertor concepts can be tested DEMO, ST

Increased connection length and flux expansion reduces heat loads

Increased connection length and flux expansion reduces heat loads

Expanded flux divertorExpanded flux divertor

Low poloidal field

Low poloidal field


MAST-U plasma modelling


Plasma scenario modelling methodology – step 1

SCENE equilibrium


Plasma scenario modelling methodology – step 1• The initial scenario was produced using the SCENE code to create a

“CTF-like” plasma:-

– Input boundary and ne, Te/Ti profiles produced from analytical expressions (using e.g. elongation/triangularity values for boundary and T0/Tped in temperature expression) informed by appropriate MAST/NSTX experimental pulses.

– Other parameters (Ip, Zeff, Irod etc) prescribed.

•Ip = 1.2MA

•Irod=2.2MA

•Zeff=1.781

•Ti=Te



SCENE equilibrium

FIESTA equilibrium guided by SCENE



• SCENE equilibrium then used to guide FIESTA modelling.

• Pressure profile used as input and a realistic coil set is used to attempt to match SCENE boundary and global parameters (kappa, li, p etc) as closely as possible.

SCENE FIESTA



SCENE equilibrium


TRANSP run from FIESTA eqm.


Plasma scenario modelling methodology – step 3• FIESTA equilibrium then used to derive inputs to TRANSP code• TRANSP used to investigate Neutral Beam requirements to

produce a fully relaxed simulation with global parameters matching the SCENE and FIESTA equilibria.

• TRANSP considered useful for NB investigation due to integrated plasma equilibrium solver and Monte-Carlo NUBEAM package.

• By specifying various NB layouts and tweaking input profiles to match SCENE/FIESTA global parameters, the NB requirements could be assessed.

• TRANSP run for a sufficient time (>5s) to reach a fully relaxed state.


TRANSP Neutral Beam investigation

2 double PINI boxes (1 on-axis, 2 off-axis PINIs. 1 unpopulated on-axis position)

1 on-axis counter-current PINI

4 beam system: 1×on-axis, 1×on-axis counter, 2×off-axis



SCENE equilibrium



TRANSP Scenario A

TRANSP Scenario B

TRANSP Scenario C

TRANSP Scenario D

TRANSP Scenario E

TRANSP Scenario F

TRANSP Scenario G

Common parameters:• Ip=1.2MA• κ=2.5• A=1.6• li(3)=0.5

(except where stated otherwise)

• A1,A2 : baseline, CTF-like q profile, 2 density variants

• B : high fast particle content - confinement, fNI=0.9, βN=6,

• C1, C2 : long pulse, fNI>1, βN=6.7, reduced TF, 2 Ip variants

• D : high βT, Ip=2MA, q0~1, test fast particle β limit

• E : 'touch-base', high li, low β

• F : high =0.6, β limit and confinement scaling

• G : high thermal βT (βN up to 7), Ip=2MA, ng=1, β limit testing

TRANSP Scenario A

TRANSP Scenario B

TRANSP Scenario C

TRANSP Scenario D

TRANSP Scenario E

TRANSP Scenario F

TRANSP Scenario G

Each scenario demonstrates a different aspect of CTF/ITER/DEMO physics.



• TRANSP pressure and current profiles then passed back to guide further FIESTA modelling using a modified coil set (engineering design evolved since last modelling round!).

• New boundary passed to TRANSP model.• In principle this iteration could continue but it was

considered that no significant improvements to the boundary or pressure profile would result.


Plasma scenario modelling methodology

SCENE equilibrium



TRANSP Scenario A

TRANSP Scenario B

TRANSP Scenario C

TRANSP Scenario D

TRANSP Scenario E

TRANSP Scenario F

TRANSP Scenario G

Pressure Profile + updated coil set

Sensitivity studies Time evolution studies Stability studies


Sensitivity studies


Sensitivity studies

• Equilibria presented are based on carefully chosen assumptions.– Necessary to test how scenarios react to changes in these

assumptions.

• NB layout based on engineering considerations– Necessary to test that layout chosen is sufficiently close to

optimum for physics.


Sensitivity studies Ex 1 – Te/ne profile peaking• Te/ne profiles are assumed to be achievable based on observation of

MAST/NSTX plasmas.• In practice there is a risk of the profiles being more peaked. What is the

effect on the baseline scenarios?

• Simple peaking algorithm applied to ne profile, scaling applied to keep line average ne constant and Te adjusted to maintain H98~1.

• Simple peaking algorithm applied, Te scaled to maintain H98~1.


Sensitivity studies Ex 1 – ne profile peaking Scenario

Parameter

Sc A with very peaked density

IP 1.2MA 1.2MA

B0 0.78T 0.78T

ne(0)/<ne> 1.13 1.78

H98 1.03 0.92

q0

qmin

q95

2.32 2.12 8.71

2.23 1.74 8.35

95 0.37 0.33

95 2.48 2.48

t 11% 11%

p 1.48 1.66

Nthermal 3.16 2.90

fbs 0.29 0.31

fNBCD 0.15 0.21

Some risk to scenario as qmin drops below 2 but is still above 3/2

Non-inductive current drive increases

q-profile with flat and peaked density profiles


Sensitivity studies Ex 1 – Te profile peaking

Scenario

Parameter

Sc A With very peaked temperature

IP 1.2MA 1.2MA

B0 0.78T 0.78T

Te(0)/<Te> 1.53 2.88

H98 1.03 1.00

q0

qmin

q95

2.32

2.12

8.71

1.12

0.94

7.53

95 0.37 0.27

95 2.48 2.48

t 11% 12%

p 1.48 2.11

Nthermal 3.16 3.22

fbs 0.29 0.27

fNBCD 0.15 0.13

Catastrophic drop in q-profile, qmin <1

Reduction in non-inductive current

Such highly peaked Te unlikely due to H-mode profile shape (generally much flatter in H-mode) and off-axis heating from off-axis NBI.


Sensitivity studies Ex 2 - PINI position and Tangency radius

• A single PINI is defined for the TRANSP run.• Vertical position and tangency radius (using horizontal

LOS) varied to obtain total Ibeam and electron/ion heating from a PINI in a wide range of positions.

• Equilibrium shape differs only a little from the baseline scenario so, although most of the parameters from the run are unrealistic (, H98 etc), the beam driven current, shine-through and heating power is reasonably reliable.


Sensitivity studies Ex 2- PINI position and Tangency radius

• Scenario A beam driven current presented. (Other parameters such as heating power, shine-through etc can also be determined.)

•Contours show total Ibeam for a PINI in a particular Z/RTan position. This is NOT a map of Ibeam contours in the plasma!

Simulation indicates more efficient beam current drive may be realised with beams at higher RTan

Total Ibeam/PINI

RTan (m)

Z (m)


Sensitivity studies Ex 2 - PINI position and Tangency radius

• Studies on all Baseline scenarios showed a clear advantage to increasing RTan for some PINIs.

• New configuration specified as:

• Different PINI positions produce an NB system with greater flexibility.

Z (cm) RTan (cm)

Off-axis 1 65 90

Off-axis 2 65 80

On-axis 0 90

On-axis

(cntr.)

0 -70


Other sensitivity studies• A number of other sensitivity studies have been

carried out including:– Plasma rotation (eqm. assumption test)– Ti scaling (eqm. assumption test)– PINI power scaling (q-profile control)– Anomalous Fast Ion diffusivity (MHD sensitivity)– Reduced number of PINIs (project staging approach)– Increased number of PINIs (project staging approach)

• Whereas assumptions used to set up the TRANSP model, particularly Te and ne shape, introduce uncertainties into the results…

• Uncertainties can be mitigated by carrying out sensitivity studies allowing optimum engineering decisions to be made.


ASTRA studies

O. Zolotukhin


ASTRA studies• ASTRA is a 1.5D transport code

– Core transport properties determined by turbulence-driven transport coefficients from GLF23

– Pedestal zone described by critical pressure gradient from empirical MAST scaling and width ~

– For this study it has been coupled with the ESC 2D equilibrium code and the NUBEAM Monte-Carlo neutral beam code

• Parameters taken from appropriate TRANSP run to set-up ASTRA model:

– ne profile

– Ip, Zeff, boundary etc

– Temperature edge value set to 0.175 - 0.4keV to simulate H-mode, Te profile calculated

• Studies

– Scenario D: time evolution during Ip ramp-up and to stationary state.

– Scenario A: sensitivity to temperature boundary conditions– Scenario A: Calculated plasma density profile

pol


ASTRA studies – scenario D time evolution

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.4

0.8

1.2

1.6

2.0

n

D Ip

I p (M

A)

t (s)

0

2

4

6

8

10

n (

10

19m

-1)

Ip and ne ramp to flat-top values by 300ms

0.0 0.5 1.0 1.5 2.0 2.50

1

2

3

4

0.0

0.2

0.4

0.6

0.8

Wtherm

Ti0

Te0

D

Te

0, T

i0 (

keV

)

t (s)

Wth

erm (

MJ)

0.0 0.5 1.0 1.5 2.0 2.50

1

2

3

4

li(3)

q0

D

q 0, l

i(3)

t (s)

0.00

0.02

0.04

0.06

0.08

E

E (

s)

Core temperature and stored thermal energy equilibrate by 800ms

Current profile equilibrates after 2.5s

0.0 0.5 1.0 1.5 2.0 2.50.0

0.4

0.8

1.2

1.6

2.0

Ip

I p (M

A),

(Vs)

t (s)

Flux consumption reaches limit after 2.5s

• Run to fully relaxed state should be possible for high-current scenario


ASTRA studies – Scenario A boundary conditions

0.0 0.1 0.2 0.3 0.40

1

2

3

10

20

30

Te0

/Tea

Te0

/Tea

Te0

Te0

(ke

V)

Te,i

(a) (keV)

0.00

0.03

0.06

0.09

E (

ms

)

Reference value in [1]

L

A1

E

H

0.1 0.2 0.3 0.40.0

0.2

0.4

0.6

0.8

fCD

fbs

fbs

+fCD

frac

tions

of d

rive

n cu

rren

t

Te,i

(a) (keV)

A1Reference value

in [1]

• Pedestal temperature varied in model (ref: 175eV) to determine scenario sensitivity

Change of Te0 and Te0/Tea with Tea define boundary between L and H mode

Change in current drive efficiency less sensitive to boundary values in H-mode

• With scenario in H-mode, lower than expected boundary temperature does not result in catastrophic loss of non-inductive current drive.


ASTRA studies – Scenario A density profile calculation

• Previous studies have used prescribed density profile.

• Addition of particle flux term allows density to be calculated along with temperature using specified pressure parameters.

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

a)

0.5 s 1 s 2.5 s prescribed

A1

n (

1019

m-3)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

b)

t=2.5 s

model for density prescribed density

A1

Te (

keV

)

Stationary state density profile more peaked than prescribed Te profile agrees well

• More peaked density profile may occur than is presently accepted in the baseline model

• Earlier sensitivity study indicated moderate density peaking can easily be tolerated


MHD stability studies

I. Chapman, S. Pinches,

S. Saarelma


MHD Stability• Studies have been carried out using the

MISHKA MHD code to test stability of the scenarios to all MHD modes

• Stability of the Baseline scenarios has been investigated

• It has been found in all cases the most problematic instability is an n=1 internal kink mode (so called “infernal” mode)

• Stabilisation effects of rotation, conducting wall structures and triangularity variation have been investigated.


MHD Stability – Rotational stabilisation• Example: Scenario C is most challenging with a calculated N limit of

4.0 and a target N of 6.7

• TRANSP rotation model and prescribed rotation profile used:

• Rotation stabilises the n=1 mode but, for Scenario C, it is unlikely rotation alone will be sufficient to reach the target N.


MHD stability – stabilisation plates• Conducting 1st wall and structures in the vessel can have a stabilising

influence.

• MAST vessel is large wall is far from plasma⇒• Stabilisation plates can be included in the design

• Stabilisation plates significantly improve limit of n=1-3 modes (“plates 3” is the realistically achievable preferred option)


• Tests carried out on Scenario C, triangularity varied between =0.3 and =0.72 (reference =0.52)

• N is varied and the limit taken to be the value where growth rate of the n=1 mode becomes positive.

• Significant increase in the limit is seen with increased triangularity

• Divertor upgrade (more divertor coils) should assist in exploiting this mechanism

MHD stability - triangularity


Conclusions


Conclusions• A set of baseline scenario models have been produced in

support of the MAST-U physics case.• Testing neutral beam layouts has optimised the MAST-U design

for non-inductive current drive and heating.• A series of sensitivity studies has demonstrated the scenarios

are robust with respect to initial assumptions and temperature pedestal height.

• Transport modelling of the startup phase has shown the increased flux available is sufficient to reach a fully relaxed state in the demanding high Ip scenario.

• Modelling of density profile broadly agrees with assumed densities with the possibility of moderate profile peaking

• MHD stability has been assessed and mitigating effects of plasma rotation, stabilisation plates and plasma shaping have been investigated.


END

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International Spherical Tori Workshop 2009, Madison, WI1 Modelling plasma scenarios for MAST-Upgrade Neutral beam requirements, sensitivity studies and