Ohmic Heating

I ntroduction to Nuclear Fusion

Prof. Dr. Yong-Su Na

2

How to heat up a plasma?

http://iter.rma.ac.be/en/img/Heating.jpg 3

Plasma Heating

4

Ohmic heating

5

Electric blanket

• Intrinsic primary heating in tokamaks due to Joulian dissipation generated by currents through resistive plasma:

thermalisation of kinetic energies of energetic electrons

(accelerated by applied E) via Coulomb collision with plasma ions

• Primary heating due to lower cost than other auxiliary heatings

Ohmic Heating

Auction (Korea)

6

I_p

I_CS

F

I_CS I_p

dt V d

R dt I

L

_p

dI

^p



_{p p}



_p

  

http://en.wikibooks.org/w/index.php?title=File:Transformer.svg&filetimestamp=20070330220406

V_p

Ohmic Heating

7

Magnetic field limited by engineering

→ compact high-field tokamak

2 2

/ 3 5

2

) 2 / (

10 1 0

.

1 



 



 



 





 



 



 







R B q

q q T

j Z P

o a

o

eff 



q₀, q_a limited by instabilities - Z_eff limited by radiation losses

- High T required for enough fusion reactions

Ohmic Heating

E

L

nT

P  3 / 



5 4 5

2

0

10

8

7 .

2 



 



 



 



 

 R

B q

nq T Z

a E

eff





2 / ) 10 /

( n

²⁰

a

²

E





5 .

1

Zeff q_aq_o 1.5

Alcator scaling

5 4

87 .

0 B

_

T 

8

Average temperatures above ~ 7 keV are necessary before alpha heating is large enough to achieve a significant fusion rate.

2 2

/ 3 5

2

) 2 / (

10 1 0

.

1 



 



 



 





 



 



 







R B q

q q T

j Z P

o a

o

eff 



 

in

e e i i in in

E P

T n T n P

W t

P W

W 







 

 3/2

Ohmic Heating



Weston M. Stacey, “Fusion Plasma Physics” WILEY-VCH (2005)

9

It seems unlikely that tokamaks that would lead to practical reactors can be heated to thermonuclear temperatures by Ohmic heating!

Ohmic Heating

E

L

nT

P  3 / 



5 4 5

2

0

10

8

7 .

2 



 



 



 



 

 R

B q

nq T Z

a E

eff





2 / ) 10 /

( n

²⁰

a

²

E





5 .

1

Zeff q_aq_o 1.5

Alcator scaling

5 4

87 .

0 B

_

T 

2 2

/ 3 5

2

) 2 / (

10 1 0

.

1 



 



 



 





 



 



 







R B q

q q T

j Z P

o a

o

eff 



Weston M. Stacey, “Fusion Plasma Physics” WILEY-VCH (2005)

 

in

e e i i in in

E P

T n T n P

W t

P W

W 







 

 3/2



10

Neutral Beam Injection (NBI)

11

Neutral Beam Injection

12

259-Car Autobahn pile-up near Braunschweig,

largest in German history:

(20 July 2009)

- More than 300 ambulances, fire engines and police cars

rushed to the scene to tend to the 66 people injured in the crash.

- The crash was blamed on cars aquaplaning on puddles and a low sun hindering drivers.

Neutral Beam Injection

13

Neutral Beam Injection

14 Andy Warhol

http://www.nasa.gov/mission_pages/galex/20070815/f.html

Plasma

NBI

Neutral beam

• Supplemental heating by energy transfer of neutral beam to the plasma through collisions

• Requirements

- Enough energy for deep penetration - Enough power for desired heating

- Enough repetition rate and pulse length > τ_E

Neutral Beam Injection

Beam particles confined 

Collisional slowing down 

Injection of a beam of neutral fuel atoms (H, D, T)

at high energies*



Ionisation in the plasma

15

* E_b = 120 keV and 1 MeV for KSTAR and ITER, respectively

B H,D,T

Neutral Beam Injection

Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001

16

   

fast slow fast gas

D D

D

D

^



₂

 

₂^

- Charge exchange:

- Re-ionisation:

 D   D    D

^

 D  e

^

fast gas fast gas

2 2

- Efficiency: (outgoing NB power)/(entering ion beam power)

• Neutraliser

Neutral Beam Injection

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• Energy Deposition in a Plasma

Andy Warhol

http://www.nasa.gov/mission_pages/galex/20070815/f.html

n: density

s: cross section

NBI

beam energy

Attenuation of a beam of neutral particles in a plasma

http://www.doopediat.com/_upload/image1/50000/53000/400/53018.jpg

Charge exchange: D_fast  D^  D_fast^  D

Ion collision: D_fast  D^  D^_fast  D^  e Electron collision: D_fast  e  D_fast^  ee

Neutral Beam Injection

In large reactor plasmas, beam cannot reach core! 18

tot b

b

N x n

dx x

dN ( )   ( ) s

Neutral Beam Injection

• Energy Deposition in a Plasma

Charge exchange: D_fast  D^  D_fast^  D

Ion collision: D_fast  D^  D^_fast  D^  e Electron collision: D_fast  e  D_fast^  ee

- Attenuation of a beam of neutral particles in a plasma

Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001

  x N    n x 

N

_b



_b

0 exp  s

_tot

Ex. beam intensity:

I ( x )  N

_b

( x ) v

_b

 I

₀

 exp   x /  

n s

tot

  1

Penetration

(attenuation) length

2

10

20

5 m

tot





s 

3

1020

5 ^

 m

n E_b0  70keV

m

4 .

 0

19

4 ) /

( ) (

) (

10 5

. 5 1

3 17

Z a m

n amu A

keV E

Z

n

_eff

b eff

tot

 





_{  }

 s

- General criterion for adequate penetration

 eff

b

AnaZ

E  4 . 5  10

^19

Neutral Beam Injection

• Energy Deposition in a Plasma

Charge exchange: D_fast  D^  D_fast^  D

Ion collision: D_fast  D^  D^_fast  D^  e Electron collision: D_fast  e  D_fast^  ee

Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001

- Attenuation of a beam of neutral particles in a plasma

20

Neutral Beam Injection

• Energy Deposition in a Plasma

Charge exchange: D_fast  D^  D_fast^  D

Ion collision: D_fast  D^  D^_fast  D^  e Electron collision: D_fast  e  D_fast^  ee

Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001

- Attenuation of a beam of neutral particles in a plasma

21

Neutral Beam Injection

• Energy Deposition in a Plasma

Charge exchange: D_fast  D^  D_fast^  D

Ion collision: D_fast  D^  D^_fast  D^  e Electron collision: D_fast  e  D_fast^  ee

Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001

- Attenuation of a beam of neutral particles in a plasma

22

Neutraliser

D

D D₂

Low

temperature D plasma,

5 eV

Ion source

D⁺, e^-

100 kV -3 kV 0 kV Extraction acceleration grids

D⁺ D⁺ D₂⁺

Beam dump

Vacuum valve

Beam duct

Ex) W7-AS: V = 50 kV, I = 25 A, power deposited in plasma: 0.4 MW

• Generation of a Neutral Fuel Beam

Neutral Beam Injection

Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001

B

D⁺

Deflection magnet

. .

.

23

• Ion Source

Neutral Beam Injection

24

Neutral Beam Injection

• Ion Acceleration

25

• Ion Neutralisation

Neutral Beam Injection

26

• Ion Deflection

Neutral Beam Injection

27

•Neutral Injection

Neutral Beam Injection

28

• JET NBI System

Neutral Beam Injection

29

• JET NBI System

Neutral Beam Injection

JET with machine and Octant 4 Neutral Injector Box 30

• JET NBI System

Neutral Beam Injection

https://www.euro-fusion.org/eurofusion/europe-participates/czech-republic/

Octant 4 Neutal Injector Box 31

• JET NBI System

Neutral Beam Injection

https://www.euro-fusion.org/eurofusion/europe-participates/czech-republic/

32

B Tangential injection

Radial (perpendicular, normal) injection

• standard ports

• particle loss

• shine-through

B

 B

. Radial injection:

• Injection Angle

Neutral Beam Injection

Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001 , 2

2 1

B r B

v _L

B D



 

 _



v B

33

KSTAR NB shine-through armor

• Injection Angle

Neutral Beam Injection

B Tangential injection

Radial (perpendicular, normal) injection

Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001

34

JET

ASDEX Upgrade

Neutral Beam Injection