Electromagnetic Waves

(1)

I ntroduction to Nuclear Fusion

Prof. Dr. Yong-Su Na

(2)

2

How to heat up a plasma?

(3)

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

Plasma Heating

(4)

4

Wave heating by resonance

(5)

5

Tuning fork

Resonance

Electromagnetic Waves

KBS. 스펀지:목소리로 와인 잔 깨기. 2006.3.11

http://www.kbs.co.kr/end_progra m/2tv/enter/sponge/view/vod/13

86311_1027.html

(6)

6

Tacoma Narrows Bridge (1940. 11. 4)

(7)

7

Broughton Suspension Bridge

http://www.joysf.com/?mid=forum_sf&document_srl=4265290&page=5

(8)

8 http://blog.naver.com/rlhyuny27?Redirect=Log&logNo=30029307561 http://cafe.naver.com/nadobaker.cafe?iframe_url=/ArticleRead.nhn%3Farticleid=82

Microwave oven (2.45 GHz)

(9)

9

• Electron Cyclotron Resonance Heating (ECRH)

Linear / Circular polarisation

(10)

10

Excitation of plasma wave (frequency w) near plasma edge

http://www.asc-csa.gc.ca/images/radarsat2_figure2_l_h.jpg

Antenna ω

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

wave transports power  into the plasma center

(11)

11

absorption near resonance,  e.g. w  w_c ^,

i.e. conversion of wave energy into kinetic energy of

resonant particles

Resonant particles thermalise wave transports power 

into the plasma center Excitation of plasma wave (frequency w) near plasma edge

R

m qB

c  w

wc

w 

Resonance

Electromagnetic Waves zone

Antenna ω

B

w m B  q

(12)

R 12

m qB

c  w

wc

w 

Resonance

Electromagnetic Waves zone

Antenna ω

B

w m B  q

KSTAR first plasma

(13)

13

Waves in a plasma

(14)

14

t E B

t E j c

B



 









 







 



0 2

 1

• Considering externally driven perturbations in the magnetic and electric fields and in the current, relative to an

equilibrium condition for a cold plasma w/o external magnetic fields

Maxwell equation

Plasma Waves

E E

E  

) 2

( )

(    







 







 



 t

B

2 2 0 2

1 t

E c

t j



 



 



 



 ^B

t

 

 

 







j

j j

jq u

n j

j j

j j j

j j

j

j u u n q E u B p

t n u

m     



 



  



 ( ) (   )

Equations of motion:

cold plasma w/o B

m E q t

u

j j

j 



 

  ^ ^_ ^  ^_ ^ 

j j

j j j

j j

j E

m q n t

q u t n

j  

 ₂

(15)

15

Plasma Waves ^⁽^^Ê^⁾ ^^²Ê^ ^ ^^⁰ _^^_t^j ^ _c¹² ^_²_tÊ²^

2 2 2 2

0

2 1

)

( t

E E c

m q E n

E

j j



 











 











 ^ ^ ^  ^ ^ _^ ^  ^_ ^ 

j j

j j j

j j

j E

m q n t

q u t n

j  

 ₂

(16)

16

c E m E

q E n

k E

k k

j j

j

j  



 



2 2 2

0

) 2

(    w









 







 

Plasma Waves

Plane waves with space and time dependences



⁽ ⁾



exp i krwt

frequency :

vector wave

: w

k iw

k t

i  



 

 ,

2 2 2 2

0

2 1

)

( t

E E c

m q E n

E

j j



 











 











 ^ ^ ^  ^ ^

(17)

17

  ⁰

0 )

( ₂

2 2 0

2







 











 





 

E

c E m E

q E n

k E

k k

j j

 



 

  w

Determinant (...)= 0

→ Disperison relation D(w, k) = 0

Plasma Waves



⁽ ⁾



frequency :

vector wave

: w

k c E

m E q E n

k E

k k

j j

j

j  



 



2 2 2

0

) 2

(    w









 







 

2 2 2 2

0

2 1

)

( t

E E c

m q E n

E

j j



 











 











 ^ ^ ^  ^ ^

(18)

18

Plasma Waves



⁽ ⁾



frequency :

vector wave

: w

k E

k 

||

E k 



2 2

0

2 1

p

j j

m q

n w

w    

2 2

k p

c w

w  

Plasma frequency

•

Plasma wave

  ⁰

0 )

( ₂

2 2 0

2







 











 





 

E

c E m E

q E n

k E

k k

j j

 



 

  w

(19)

19

• Plasma waves are solutions of dispersion relation D(w, k)=0.

Generally:

w given by generator k_||given by antenna where k_||>k_||,Vacuum

solution: k_ = k_ (w, k_||)

Special cases:

1. k_ 0

Perpendicular to magnetic field

„cutoff“ ^reflection_tunnelling

http://www.srh.noaa.gov/srh/jetstream/atmos/ionosphere_max.htm

Dispersion Relation

2. k_  „resonance“

(20)

20 http://star.mk.co.kr/new/view.php?sc=40500009&year=2010&no=391063&mc=PT&mc=PT

Dispersion Relation

• Plasma waves are solutions of dispersion relation D(w, k)=0.

Generally:

w given by generator k_||given by antenna where k_||>k_||,Vacuum

solution: k_ = k_ (w, k_||)

Special cases:

1. k_ 0

Perpendicular to magnetic field

„cutoff“ ^reflection_tunnelling

http://www.srh.noaa.gov/srh/jetstream/atmos/ionosphere_max.htm

2. k_  „resonance“

(21)

21

Wave heating in a tokamak

(22)

22

• Ion Cyclotron Resonance Heating (ICRH):

occurring only when two or more ion species are present ω ~ ω_ci, 30 MHz – 120 MHz (λ ~ 10 m)

• Lower Hybrid (LH) Resonance Heating:

ω_ci < ω < ω_ce, 1 GHz – 8 GHz (λ ~ 10 cm)

• Electron Cyclotron Resonance Heating (ECRH):

ω ~ ω_ce, 100 GHz – 200 GHz (λ ~ mm)

i i ci

c c

ii m

eB Z Z

n Z n Z

m Z

m

m n m

n 



 w w  w

w ,

) /

/ (

) /

1 (

1 1 2 2 2

1 1 2

1 1 2 2 2

2 1

: Ion-ion resonance frequency

2 2

2

2 _pi /(1 _pi / _ce), _pi _ci

LH w w w w w

w   

2 2

2

ce pe

UH w w

w  

Electromagnetic Wave

(23)

23

Electromagnetic Wave

wLH

wce

wci

1

X (wpe2/ w²)(n_e) Y(wce/w) (B)

w_LH P = 0

O cut-off

R=0 R(X) cut-off

L=0 L(X) cut-off

m_i/m_e

S=0 X resonance

LHR L=h L resonance

R=h R resonance

ICRH LHRH

ECRH

UHRH

E.M.

E.S.

E.M.

S=0 X resonance

UHR

RF waves in Fusion Plasmas, S. H. Kim (KAERI), Seminar at SNU (2013)

(24)

24

• Wave launching, propagation, absorption in fusion plasmas

Wave System

Transmission line Matching network Wave

source Antenna

(Horn)

Vacuum window Limiter

Absorption layer

Vacuum Wave (Coupling)

Propagation

Absorption (Mode conversion)

RF waves in Fusion Plasmas, S. H. Kim (KAERI), Seminar at SNU (2013)

(25)

25

• JET ICRH System

λ ~ 10 m

Ion Cyclotron Resonance Heating

KSTAR ICRF wave generator:

Transmitter (Tetrode tube)

(26)

26

D(H) Minority Heating Scheme in KSTAR

Wang, 2009 Cut-off/Resonances in minority

heating scheme

• Propagation and absorption

(27)

JET (Start et al. 1999) 27

T 2^nd Harmonic + He3 minority Heating

• Experimental results

(28)

28 https://www.burningplasma.org/newsandevents/?article=enews&issue=081507

(29)

29

• JET LH System

λ ~ 10 cm

Lower Hybrid Heating

500 kW klystron for ITER

(30)

30

J. C. Wright, POP (2009) Petrov, CompX

Petrov, CompX

(31)

31

Y. Peysson, Fusion summer school in KAIST, 2009

(32)

• KSTAR ECH System

λ ~ mm

Electron Cyclotron Heating

32 Y. S. Bae et al, Fusion Science and Technology 52 321 (2007), 65 88 (2014)

(33)

33

(34)

34

R. Prater, Fusion summer school in KAIST, 2009

(35)

35

R. Prater, Fusion summer school in KAIST, 2009

Full non-inductive CD in TCV X2 heating in DIII-D

(36)

36

Alpha particle heating

(37)

37

• Intrinsic self-heating by Coulomb collision of fusion α particles with plasma particles in D-T reactions

) 5

. 3 ( )

1 . 14

( MeV He⁴ MeV

n T

D   

• Heating power density:

5

DT T

D

v Q N

N 

where v T_i

 peaked heating profile

leaves plasma heats plasma if sufficiently long confined

α-Particle Heating

• α-particle loss mechanisms: field ripples

MHD events e.g. Alfvèn Eigenmode (AE)

A.V. Melnikov et al, NF 53 093019 (2013)

(38)

38

• DT-Experiments only in - JET

- TFTR

• with world records in JET:

- P_fusion = 16 MW - Q = 0.64

α-Particle Heating

(39)

39

Current drive

(40)

40

Non-inductive Current Drive

Z. Gao, “Summer school in KAIST” 2009

(41)

41

• Asymmetric velocity distribution can be a side effect of plasma heating.

ions

electrons ^j ^q ⁿ_s ^v ^f

 

^v ^dv

s



|| ||





Non-inductive Current Drive

• Needed for: Steady-state tokamak

current profile control in tokamaks

bootstrap current compensation in stellarators

(42)

42

B Tangential injection

JT-60U high b_p ELMy H-mode

Neutral Beam Current Drive

(43)

43

Heating Scheme Advantages Disadvantages

OH Efficient Cannot reach ignition

NBI Reliable Close to torus,

Negative ion source necessary

LH Efficient current drive (CD)

Antenna close to plasma,

off-axis CD ECRH Reliable, Flexible

Localised CD Electron heating

ICRH Ion heating

Central heating

Antenna close to plasma,

Antenna coupling

Heating and Current Drive