IAEA divertor meeting 9 2015 v5 reduced equations - Nucleus...Institute, Russia, 5ITER IO! Detachment front location affects divertor and core plasmas! IAEA divertor mtg, Sept 29-Oct

Detachment performance & control: Where we are and where we need to be for a reactor

B. Lipschultz1

Contributions from I. Hutchinson2, F. Parra-Diaz3, A. Jarvinen4, A. Kukushkin5, R. Pitts5

Status of detachment control The importance of detachment control & present capability Analytic model to understand the relationship between different

control variables as well as the effect of magnetic topology ITER diagnostics and prospects for detachment control for ITER

and DEMO

IAEA divertor mtg, Sept 29-Oct 2, 2015 1

1U. Of York, 2MIT. 3Oxford U, 4Aalto, Finland, 5Kurchatov, Institute, Russia, 5ITER IO

Detachment front location affects divertor and core plasmas


Core

Major radius, R

Hei

ght z

Detachedregion

Detachment ‘front’

Radiation(thermal front)

a)Detachment close to the target • Maximizes He pumping • Localizes heat load due to radiation • Heat load reduction primarily near separatrix

a)Detachment close to the target • Maximizes He pumping • Localizes heat load due to radiation • Heat load reduction primarily near separatrix

b) Detachment region expanded to x-point • Maximize cooling of core plasma • Maximize impurity and neutral access to core • Maximize divertor power losses


Detachment front location affects divertor and core plasmas

Core

Major radius, R

Hei

ght z

Detachedregion



Need to control power losses as well as detachment front location

• We have only studied the effects for front locations at the x-point and target • Detachment front location control would allow the study of the tradeoff between

maximizing power loss, He pumping, erosion, and effects on core confinement ! More control needed


• Educated guess of detachment front effects ! Wide variations in the

magnitude of effects

He pumpingDivertor power losses

Core confinement lossCore impurity levels

Detachment front locationTarget

Posi

tive

Effe

ct o

n co

re &

div

erto

r pla

smas

Neg

ativ

e

0

x-point


ITER scenario* • Detached region close to the target

! Minimizes effects on the core plasma • How do we hold it there through transients

and variations in upstream characteristics?

• Next slides – status of control in present tokamaks

*A. Kukushkin, personal communication

ITER scenario (power loss, detachment front location) needs to be achieved through control

ITER line radiation calculation*

History and status of feedback control (ignoring feedforward)

Successful feedback control efforts • Divertor detachment feedback

! Limiting the seeding rate when the radiation (based on bolometry chords) reaches the x-point1,2

IAEA divertor mtg, Sept 29-Oct 2, 2015 6 1J. Goetz et al., Phys. Plasmas 6 (1999) 1899 2A. Kallenbach, Nucl. Fusion (1995)

C-Mod1




! Using thermo-electric currents to the outer divertor3 (effective Te,div) best for keeping location at target


1J. Goetz et al., Phys. Plasmas 6 (1999) 1899 2A. Kallenbach, Nucl. Fusion (1995) 3A. Kallenbach, Plasma Phys. & Contr. Fusion (2010)

AUG3




! Using thermo-electric currents to the outer divertor3 (effective Tdiv) best for keeping location at target

• Core & divertor radiation feedback using bolometry chords and effective Tdiv

4

! Separately controls of power crossing the separatix and power to the plate ~ through Tdiv, not front location


1J. Goetz et al., Phys. Plasmas 6 (1999) 1899 2A. Kallenbach, Nucl. Fusion (1995) 3A. Kallenbach, Plasma Phys. & Contr. Fusion (2010), 4A. Kallenbach et al., Nucl. Fusion 52 (2012) 122003

AUG4

Summary of detachment control

Level of control • Detachment front location control generally not directly implemented

! Generally held near detachment threshold or close to x-point detached • Difficult to integrate control of multiple control variables into detachment control • Better front location control would allow studies of the tradeoff between optimizing power

loss and minimizing the effect on the core plasma Goal of present work*: develop a physics-based model of the detachment front location to • Guide our understanding of detachment front control • Address how varying magnetic topology (*e.g. ‘alternative divertors) might improve

control and/or volumetric radiation. • Potentially contribute to advancement of detachment control algorithims relating a number

of control variables to each other

IAEA divertor mtg, Sept 29-Oct 2, 2015 9 *B. Lipschultz, F. Parra, I. Hutchinson

• Analytic model of detachment control ! Relative utility of various control variables ! Effect of magnetic configuration


Analytic detachment front model description

• Our study is built on the 1D Hutchinson model of thermal front stability1, which uses a few assumptions, similar to ‘two-point model’ and maximum radiation calculations2-5 ! Upstream, there is an energy source, S, due to cross-field transport (PSOL) ! Only the energy equation is treated (conduction) ! There is a thermal front along B, within which there is an energy sink, E, due to impurity

radiation, which lowers the target temperature enough to achieve detachment ! pressure constant along B through the thermal front up to the detached region


1Hutchinson, IH, 1994 Nuclear Fusion 34 13337, 1Lengyel, L, ‘Analysis of Radiating Plasma Boundary Layers’, Max-Planck-IPP 1/191, Garching (1981), 2Lackner K and Schneider R 1993 Fusion Eng. Design 22 107, 3Post D et al 1995 Phys. Plasmas 2 2328, 4A. Kallenbach et al, Plasma Phys. & Contr. Fusion 55 (2013) 124041

Upstream (L)

X-point

Thermalfront (E)radiation

Detachedregion

Detachment front recombinationCharge exchange

target (0)

B

Heatsource (S)

T n

losses

010203040506070

0.0 0.1 0.2 0.3 0.4 0.9 1.0

thermal front

z/L

x-po

int

T [re

lativ

e un

its]

H [r

el. u

nits

]

Th

−2

−3

−1 E

S0

Tc

Coordinate change to simplify and include B dependence

• Explicitly incorporates the dependence of heat flux on B = |B| by the following

IAEA divertor mtg, Sept 29-Oct 2, 2015 12 1Hutchinson, IH, 1994 Nuclear Fusion 34 13337

dz = Bx

Bdl; κ ≡κ ||Bx

2 / B2

q = Bx

Bq|| = −κ 0Te

5/2 Bx2

B2dTdz

;

dqdz

= −H = −(S − E)

• q has units of total heat flux. • z (and L) is flux tube volume, arbitrarily

normalized to the flux tube volume at the x-point, Bx ! Z=0 at target, =L upstream

target X-pt

Description of solution requirement

• A solution for the front location is that

IAEA divertor mtg, Sept 29-Oct 2, 2015 13 1Hutchinson, IH, 1994 Nuclear Fusion 34 13337

qi = − κ dTdz

⎛⎝⎜

⎞⎠⎟ f

~ Sdzz

L

∫

= qf = − 2κEdTfront∫

• Next step – write down descriptions of qi and qf that relate to control variables and B = |B|

target X-pt

010203040506070

0.0 0.1 0.2 0.3 0.4 0.9 1.0

thermal front

z/L

x-po

int

T [re

lativ

e un

its]

H [r

el. u

nits

]

Th

−2

−3

−1 qf=∫rad. sink

qi=∫source0

Tc

• We can directly write down the volumetric heat source S0

Assumed source source and magnetic field profile


• Assume a simple B variation in the divertor -linear variation of B along z

BBx

= BtBx

+ zzx

1− BtBx

⎛⎝⎜

⎞⎠⎟

⎧⎨⎩⎪

⎫⎬⎭⎪ for z ≤ zx

BBx

= 1 for z ≥ zx

qi = − κ dTdz f

⎛

⎝⎜⎞

⎠⎟~ Sdz

zx

L

∫ = S0 (L − zx )

qi ∝PSOL 010203040506070

thermal front

x-po

int

T [re

lativ

e un

its]

H [r

el. u

nits

]

Th

−2

−3

−1 qf=∫rad. sink

qi=∫source0

Tc

0.0Bt

Bx

0.1 0.2 0.3 0.4 0.9 1.0z/L

B [re

l. un

its]

Radiative losses in front described as has been done by many authors (B dependence included)


• Using the radiation cooling function, Lz(T), impurity concentration, fz, and density, the integral of the total radiative energy loss, qf, can be calculated

• Standard technique for calculating the maximum amount of radiation along B1-4

! However. because we are interested only in detachment we assume that radiation lowers the temperature at the end of the thermal front to that needed for detachment.

• nu and Tu are upstream values of density and temperature

qf = − κ dTdz

⎛⎝⎜

⎞⎠⎟ front

~ − 2 fznu2Tu

2 2κT 5/2 Lz (T )T 2 dT

front∫

1Lengyel, L, ‘Analysis of Radiating Plasma Boundary Layers’, Max-Planck-IPP 1/191, Garching (1981). 2Lackner K and Schneider R 1993 Fusion Eng. Design 22 107, 3Post D et al 1995 Phys. Plasmas 2 2328, 4A. Kallenbach et al, Plasma Phys. & Contr. Fusion 55 (2013) 124041

Radiative losses characterized in terms of control variables


• U collects constants • Bx = |B| at x-point; Bf = |B| at thermal front • Since |B| ~ 1/R, then Bx/Bf ~ Rf/Rx

• Substituting in the B and 𝜅 dependence as well as Tu

qf ∝−Ufz1/2nu

Bx

Bf

PSOL2/7

Dependencies on the magnetic field in the front, Bf, and divertor flux tube length also delineated


• U collects constants • Bx = |B| at x-point; Bf = |B| at thermal front • Since |B| ~ 1/R, then Bx/Bf ~ Rf/Rx

• We have now isolated the control variables, C= nu, PSOL, and fz, the impurity concentration

! Shows the relative effectiveness (figures following) of different control variables ! Increasing Bx/Bfront strongly increases divertor radiation, qf, for fixed control variables ! Terms inside [….]2/7 of lesser importance ! Other control variables (e.g. neutral density) are important* but not included

• Substituting in the dependence of Tu on PSOL and B:

*Kukushkin, this meeting, Krashennikov, this meeting, S. Togo et al, Plasma Fusion Research 8, 2403096 (2013)

qf ∝−Ufz1/2nu

Bx

Bf

PSOL2/7

Stability of front

! The front location is stable to perturbations if

! The front position returns to the same spot if perturbed

• All front locations for the outer divertor leg are stable for assumptions of model. ! Not true for the inner divertor


ddz f

qi − qf( ) ≤ 0

Upstream (L)

X-point

Thermalfront (E)radiation

Detachedregion

Detachment front recombinationCharge exchange

target (0)

B

Heatsource (S)

T n

losses

‘Detachment window’ quantifies the level of detachment front location control


• We define a ‘Detachment window’ of control variable C: ! This is the range in C between the onset of

detachment at the target, Ct

Core

Major radius, R

Hei

ght z

Detachedregion



‘Detachment window’ quantifies the level of detachment front location control


• We define a ‘Detachment window’ of control variable C: ! This is the range in C between the onset of

detachment at the target, Ct, and when the detached region has expanded to the x-point region, Cx. ● For the example of detachment window in

upstream density, Cx – Ct = nux – nut

Core

Major radius, R

Hei

ght z

Detachedregion



Detachment window for control is dependent on zx/L and Bx/Bt


• We solve for the detachment window in upstream density, nu: qi = qf: ! [Bf,zf] = [Btarget, 0] for the front at the target and ! [Bf,zf] =[Bx, zx] for the front at the x-point

Δ !nu = nux − nut( ) / nut

• We normalize the detachment window to nut:

Strongest expansion of detachment window due to Bx/Bt, followed by zx/L


• Normalized detachment window, ∆nu, small for conventional divertor topologies (Bx/Bt~1)

• Increasing divertor leg length, zx/L (‘poloidal flux expansion’ or just longer leg length), widens the detachment window ! Most effective at low Bx/Bt (conventional

divertor) ! Not due to an increase in radiating volume

• Increasing Bx/Bt (‘total flux expansion’) strongly increases the detachment window ! Said another way, increasing Bx/Bt expands

the utility of the control variable

0

1

2

3(a)

(b)

∆nu=

(nu,

t-nu,

x)/n

u,t

1.0 1.5 2.0 2.5 3.0Bx/Bt

0

4

8

12

16

∆nu/∆n

u(B x

/Bt=

1)

zx/L =0.2zx/L =0.4zx/L =0.6 ~

~~

~

• All detachment front locations between target and x-point are stable for Bx/Bt ≥ 1

~

Detachment window in impurity concentration larger than for nu and PSOL

• We can compare the detachment window, ∆C, for all control variables,

• Detachment window increased most strongly for fz, followed by PSOL and nu ! Increasing toroidal flux expansion, Bx/Bt

enhances the utility of all the control variables studied so far

! Certainly other variables can be important as well (e.g. neutral density in the divertor*)


2

0

4

6

8

10

∆C∆C

/∆C

[Bx/B

t = 1

] nufiPSOL

1.0 1.5 2.0 2.5 3.0Bx/Bt

0

10

20

30

a)

b)

~~~

~

Δ !nu = nux − nut( ) / nutΔ!fz = fzx − fzt( ) / fztΔ !PSOL = PSOLt − PSOLx( ) / PSOLx

*M. Kotschenreuther et al., Phys. Plasmas 20 (2013) 102507, A. Kukushkin, this meeting, S. Krasheninnikov et al, J. Nucl. Mater. 266-269 (1999) 251

Aside: define poloidal and total flux expansion


Core

X 2

X 1SOL

Secondaryseparatrix

Primaryseparatrix

W. Vijvers, Nucl. Fusion 54 (2014) 023009 M. Kotschenreuther et al. Phys. Plasmas 20, 102507 (2013)

• Poloidal flux expansion, corresponding to local reductions in the poloidal magnetic field, leads to longer field line length (and thus volume) in the divertor (zx/L) ! Near the x-point(s) for the ‘Snowflake’ configuration ! Near the target for the ‘X-divertor’

Snowflake

X-divertor

Aside: define poloidal and total flux expansion


• Poloidal flux expansion, corresponding to local reductions in the poloidal magnetic field, leads to longer field line length (and thus volume) in the divertor (zx/L) ! Near the x-point(s) for the ‘Snowflake’ configuration ! Near the target for the ‘X-divertor’

• Total flux expansion, corresponding to moving the target to larger R and thus larger Bx/Bt, leads to larger flux tube area (and thus volume) in the divertor

‘Detachment front sensitivity’ gives a local (in z) sensitivity of the front location to control

• ‘Detachment front sensitivity’ : dzf/dC, where zf is the distance (volume) of the front along a field line from target towards the x-point ! Useful for controlling the front as a function

of position ! Lower sensitivity is better ! The shape of dzf/dC will change with different

assumptions for B(z)


0

1

2

3

4

5

a)

b)C/Ct

nufiPSOL

Bx/Bt=2

Target x-pointzf/L0.00 0.05 0.10 0.15 0.20

-0.3

0.3

-0.2-0.1

0.10.2

0.0

Cd(z f/L)/dC

Model implications: Radiation increases with total flux expansion


• Total radiation, qf, increases as Bx/Bf (increased total flux expansion); thermal front (target) is moved to larger R

qf ∝Bx

Bfront

Model implications: Radiating volume increases with total flux expansion


• Total radiation, qf, increases as Bx/Bf (increased total flux expansion); thermal front (target) is moved to larger R

• Increasing total flux expansion (Bx/Bt) leads to increases in both the radiating region length, ∆lf, and area, Af ! Radiating volume, Vf, increases as (Bx/Bfront)2

● Stabilizing effect of total flux expansion ! The emissivity decreases with total flux expansion ∝

(Bx/B)-1 to keep qf = qi • Front length, ∆lf, decreases as 1/|qi|

Δl f ∝Bx

Bfront qi

Af ∝Bx

Bfront

Vf ∝1qi

Bx

Bfront

⎛

⎝⎜⎞

⎠⎟

2

qf ∝Bx

Bfront


• The inner divertor target ! typically Bx/Bt < 1; ‘flux contraction’ ! More difficult to obtain stable

solutions ! => move inner divertor target to Rt>Rx

leads to stable fronts, better control and increased target area

Core

Major radius, RH

eigh

t z

Model implications: Having the inner divertor at smaller R can lead to lack of stable solution

Model implications: Having the inner divertor at smaller R can lead to lack of stable solution


• The inner divertor target ! typically Bx/Bt < 1; ‘flux contraction’ ! More difficult to obtain stable

solutions ! => move inner divertor target to Rt>Rx

leads to stable fronts, better control and increased target area*

*S. McIntosh et al, IAEA 2014, FIP/P8-9

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

zx/L

B x/Bt

Stable

Unstable

• ITER and DEMO control ! What to control and relevant diagnostics ! Diagnostic and actuator issues


ITER diagnostics for control


What to control & potentially useful diagnostics • ‘Locate front’

! 2D imaging of divertor region ! 1D measurement from Thomson scattering ! 2D from triangulation of spectroscopy chords

Divertor TS (Te, ne)

R. A. Pitts, Plasma Control System CDR, Chateau de Cadarache 13-15 November 2012

Langmuir probes (particle flux,Te, ne) IR surface heat flux

ITER diagnostics for control

What to control & potentially useful diagnostics • ‘Locate front or detached region’

! 2D imaging of divertor region ! 1D measurement from Thomson scattering ! 2D from triangulation of spectroscopy chords ! 2D map from inversion of bolometry chords

• Power loss in the divertor (& heat load) ! IR measurement of target power level ! Total radiation from core bolometer array

• Power loss inside the separatrix ! Total radiation from core bolometer array

• Neutral leakage from the divertor and He pumping ! Vessel, divertor & pump pressure gauges

IAEA divertor mtg, Sept 29-Oct 2, 2015 33 A. Suarez, 1st EPS Conference on Plasma Diagnostics April 14-17, 2015, Frascati, Italy

Langmuir probes (particle flux,Te, ne) IR surface heat flux

Divertor TS (Te, ne)

R. A. Pitts, Plasma Control System CDR, Chateau de Cadarache 13-15 November 2012

Feedback control becomes more difficult as we move to ITER and then DEMO

Diagnostic issues • Which diagnostics will be dependable

! Coatings on lenses and mirrors ! Damage to optical elements or things like Langmuir probes

• Time scales for response of actuator ! Gas injection will have a longer response time as we move to larger machines

● Reduced by mixing seeding and D gases • Seeding gases pumpout time

! Rare gases (e.g. Ar, Ne) pump away slowly ! ‘Non-recycling’ gas levels (e.g. N2) can be reduced by turning off the injection

● But N builds up over time and makes T extraction more difficult • What if diagnostic fails during a pulse

• These and other issues to be discussed in session planned for later this week


Summary

• If DEMO is similar size to ITER (ideally smaller) then power handling of the divertor must be increased - even assuming more core radiation ! Control of detachment extent (front location) is central to ITER and DEMO

● Mimimize effects of detachment on the core ● Maximize volumetric power loss, divertor lifetime and He pumping

• Analytic model results ! For fixed upstream conditions total flux expansion in the divertor

● increases the detachment window (control) by factors of 20-30 ● Integrated radiation increases as Bx/Bt

● Radiating volume increases as (Bx/Bt)2

● Radiation front length ∝ (Bx/Bt)/|qi| ! Increasing flux tube length in the divertor (zx/L) most effective at low Bx/Bt

! Model predicts the relationship between control variables and their relative effectiveness ● Useful for developing control algorithms including multiple control variables


Documents

IAEA divertor meeting 9 2015 v5 reduced equations - Nucleus...Institute, Russia, 5ITER IO! Detachment front location affects divertor and core plasmas! IAEA divertor mtg, Sept 29-Oct