FRT2-2020-7-Operation limits.pdf

F usion Reactor Technology 2

(459.761, 3 Credits)

Prof. Dr. Yong-Su Na

(32-206, Tel. 880-7204)

Operation Limits

2

• Density ranges in a tokamak discharge

- There exist a lower and an upper density limit at a given I_p.

• High densities

- atomic processes (radiation, CX, neutral atom ionization) at the plasma edge become rather important

- atomic processes can lead to contraction of the plasma column (decrease of the effective plasma radius)

→ danger of kink instability becomes real

• Low densities

- e-i collision frequency not sufficient to prevent

the generation of run-away or accelerated electrons - run-away electrons produced by the inductive E field - run-away electrons spoil the discharge characteristics and may be dangerous for the vacuum chamber

3

• Assumptions

- Circular CX, steady-state with purely OH heating, T_e = T_i = T, no impurities, atomic processes not important (radiation,

recycling, etc), fully ionized hot plasma

- Under these conditions, one can expect the existence of self- similar self-organized plasma states, if they have the same macroscopic non-dimensional parameters.

Operation Limits

4

• Murakami and Hugill Numbers - consider atomic processes

- To evaluate the role of atomic processes appropriate power losses with Joule heating power should be compared.

Introduce atomic units for length, velocity, energy Coulomb logarithm

Losses due to radiation and ionization

Operation Limits

3 . 12

~

*

/ L

T T  

_a

2 2 2 0

2 4 *

2 3

0 2

2

( )

R q T B

e F m

h L R

q B ne

j m P

a T e

a T ei

e

OH

 

    





 



 



2 4 2

2 2

,

, h

e m h

v e e

m

r h

_{a a} ^e

e

a

   

   

_*

2 2

* 2

2

G T

m h n e

T G v

r n P

e a

a a

R

  

T n e m m

B B

R

a , ,

_T

,

_p

,

_e

,

_i

, , ,

Dimensional Analysis of Tokamaks

5

- If P_R becomes comparable to P_OH,

atomic processes start to play a significant role.

- The role of atomic processes is defined by a non-dimensional parameter H (Hugill number): as increasing H, the role of atomic processes increases compared with OH heating

Murakami number If L = 12.3

 

_*

 

_*

2

/

/ P H G T F T

P

_{R OH}



c h e L

B

R nq H e

T a

2

, 

  

T a

B R H  nq

B

T

M  nR

Operation Limits

6

• Hugill plot

- limited operational region on the current-density plane - non-dimensional current .VS. non-dimensional density

Murakami number gradient:

non-dimensional density

non-dimensional current

B

T

R M  n

IR B a a

I R

aB RB

q aB

^{T T}

p T a

0 2

0

2 2

/ 





 





c T

a

I

I R

B a

I

q  

0

2

/

2 1





R nq

B

H _a

 T

1

Operation Limits

7

• Hugill plot

- Tokamak operational domain on the current-density plane is restricted by four limits.

1: limit of run-away electrons at low density

2: current limit due to the MHD-instability

3: Murakami limit at high density

(at the maximal permissible plasma current): radiative power balance 4: Hugill density limit where

H (H = q_efM) remains constant (n~I):

confinement/disruptive limit gradient:

non-dimensional density

non-dimensional current

- The limiting density is determined by the power balance on the plasma periphery (by balance of the energy flow from the central region and radiation and ionization losses).

- The density limit usually increases with additional heating as P^1/2. R

nq B

H _a

 T

1

e thermal

e T m

v en

j/   2 /

Operation Limits

8

• Hugill plot

- Tokamak operational domain on the current-density plane is restricted by four limits.

1: limit of run-away electrons at low density

2: current limit due to the MHD-instability

3: Murakami limit at high density

(at the maximal permissible plasma current): radiative power balance 4: Hugill density limit where

H (H = q_efM) remains constant (n~I):

confinement/disruptive limit

- The limiting density is determined by the power balance on the plasma periphery (by balance of the energy flow from the central region and radiation and ionization losses).

- The density limit usually increases with additional heating as P^1/2.

e thermal

e T m

v en

j/   2 /

Operation Limits

9

• Hugill plot

- limited operational region on the current-density plane - non-dimensional current .VS. non-dimensional density

10

- The two dashed lines illustrate the density limits in earlier OH/ICRF and NBI experiments with a mainly carbon 1st wall.

- When heating power is increased, the Hugill limit shifts towards higher densities.

• Hugill plot

- Attaining high densities by using beryllium coating of the chamber

wall in JET and with the help of pellet injection in JT-60U

ITER Physics Basis, Nuclear Fusion 39 2261 (1999)

1 – gas puffing, 2 – minor pellets, 3 – large pellets, Full circles – limiter, open circles - divertor

Operation Limits

11

• Hugill plot

- Attaining high densities by using beryllium coating of the chamber

wall in JET and with the help of pellet injection in JT-60U

Operation Limits

Operation Limits

12

• Hugill plot

- limited operational region on the current-density plane - non-dimensional current .VS. non-dimensional density

J. T. Scoville, Nuclear Fusion 31 875 (1991)

D = H

Operation Limits

13

• Hugill plot

- limited operational region on the current-density plane - non-dimensional current .VS. non-dimensional density

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0

0.1 0.2 0.3 0.4 0.5 0.6

RMP(n=1) locked mode disruption RMP(n=2) locked mode disruption Density limit disruption

Dedicated Runaway electron shots H-mode L-mode

I p*R/(5*a*b*B t)

n*R/B_t

Operation Limits

14

• Greenwald density limit

Greenwald limit

- For stability observations yield the conditions

IR B a a

I R

aB RB

q aB

^{T T}

p T a

0 2

0

2 2

/ 





 





T T

a

B

R n M

B a

IR

q 2 15 15

1

2

0

 

 



20 2

a n I

 

2

2

,

20

 q

_a



a n I



Basic Tokamak Variables

• Greenwald density

15

Basic Tokamak Variables

16

- As the limit is approached, the plasma becomes increasingly susceptible to disruption and data become sparser.

M. Greenwald et al, NF 28 199 (1988): one of the most cited paper in NF Martin Greenwald, PPCF 44 R27 (2002)

• Greenwald density

a

2

n

_G

I

^p

 

Basic Tokamak Variables

17

• Greenwald density

Y. Sakamoto et al, PFR 5 S1008 (2010) H. Urano et al, PPCF 44 11 (2002)

Operation Limits

18

• Pressure Limit

- related to the ballooning instability occurring due to convex magnetic lines of the outer region:

swelling on magnetic surface at the high pressures

- force balance between the cause for swelling (plasma pressure gradient) and the magnetic tension

g = β_N: Troyon factor

qR B a

p

_T

0 2

2 



N T

T T

c

aB gI g I

IR R

B a

a qR

a B

p











/ 2

2

/

₀ ² ₀

2

  



R a I

I aB

I I

c T

N

0

2



 

 I

I IR

B

q  a

^T



^c

0

2

2





Operation Limits

19

Operating range of high beta discharges in PBX compared to calculated stability limits, including the ideal n = 1 external kink limit with a conducting wall at twice the plasma minor radius and without a wall

E. J. Strait, Phys. Plasmas 1 1415 (1994)

ITER Physics Basis, Nuclear Fusion 39 2261 (1999)

T N

c

aB

 I

 

Operation Limits

20

• Pressure Limit

- If g is constant, for the most effective use of the B_T

it is preferable to have the values of β as high as possible.

→ high I_N

• Since I/I_c is limited by the upper current limit on the Hugill diagram, κa/R should be maximized.

→ The column should be elongated vertically as much as possible.

• The experimental data for critical β are summarized by a simple empirical formulae

R a I

g I gI

c N

c

0

2



   

T i

T N

c

aB

l I aB

I  4

 



Operation Limits

21

E. J. Strait, Phys. Plasmas 1 1415 (1994) ITER Physics Basis, Nuclear Fusion 39 2261 (1999) i

N

 4 l



Operation Limits

22

• DIII-D hybrid modes

limited by tearing modes limited by fishbones limited by sawteeth q₉₅=3.2, β_N=2.7, H_89P=2.3 q₉₅=3.6 without sawteeth

q₉₅>4 without sawteeth

PLASMA CURRENT(0.1MA)

NBI power (MW) 4xli (internal inductance )

β_N

Amplitude of magnetic fluctuations at the vacuum vessel

23

Operation Limits

• Pressure Limit

- Fundamental elements affecting the _N-limit 1. Current profile

2. Pressure profile 3. Plasma shape 4. Stabilising wall

p t t

N

I

 aB

 

24

• High β_N in KSTAR

1. Strong plasma shaping (PF/CS system capability) 2. Passive stabilizers

3. High heating power 4. RWM control coils

Operation Limits

• Pressure Limit