t. hellsten iea burning plasma workshop, july 2005 tarragona spain integrated modelling of icrh and...
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T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Integrated Modelling of ICRH and AE Dynamics
T. Hellsten, T. Bergkvist, T. Johnson and M. Laxåback
Alfvén Laboratory, Royal Inst. of Technology,
SE-100 44 Stockholm, Sweden Association Euratom-VR.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
ICRH is a versatile heating method that can provide:
Heating
Enhance fusion reactivity
Drive Currents
Induce rotation
Excite AEs
ICRH
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
ICRH requires self-consistent modelling of distribution functions and wave field; including effects of finite orbit width and RF-induced spatial transport of fast ions for waves with finite n.
Due to the different time scales this can be done by iterations.
ICRH Modelling
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
1 LION code L. Villard et al, Computer Physics Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173
Define equilibrium, antenna spectrum, power.
Calculate the dielectric tensor and wave field for ICRH (LION code1) from the output of FIDO
Calculate changes in orbit invariants by collisions, and ICRH with the FIDO code. Remove lost ions, add NBI, -particles and edge source.
Create tables for the various interactions used in the Monte Carlo code with an orbit solver.
Output
The SELFO code calculates the ICRH wave field with the LION code and the distribution function in the invariant space (W, P, ) with the Monte Carlo code FIDO.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
-90o phasing: trapped 3He ions displaced outwards. emission from turning points of trapped ions at
cyclotron resonance
+90o ICRH phasing:
trapped 3He orbits pinched,
then detrapped to co-current wide passing orbits at the low field side of the center
RF-induced pinch and detrapping of the orbits
T. Johnsson et al, IAEA Technical Meeting, Gothenburgh, 2001
Tomographic reconstruction of the -emission profiles from JET
Tomegraphic reconstruction by C. Ingesson
T. Hellsten et al Phys. Rev. Lett 1995
CoCounter
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Comparison of the gamma emissitivity in the mid-plane z=0 between tomographic reconstructions (full line) dashed region (confidence interval) and the density of high-energy 3He ions calculated with the SELFO code (boxes)
+90-phasinglocation of the excited TAE modes indicated
-90-phasing
SELFO code modelling by T. Johnson
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
The excitation of Alfvén eigenmodes is sensitive to the details of the distribution function.
AEs excited in JET during ICRH with +90° and -90° phasing of the antennas
+90° -90° L.-G. Eriksson, et al Phys Rev. Lett 81 (1998) 1231M. Mantsinen et al Phys. Rev. Lett. 84(2002).
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Splitting of the mode frequency
A. Fasoli et al Phys. Rev. Lett. 81(1998)5564
Fast damping when ICRH is switched off
The AEs are damped in a time period of about 0.1ms after the ICRH is switched off.
K. L. Wong,et al Phys. Plasmas 4 (1997) 393
Typical mode splitting of about 2kHz is seen during ICRH.The spitting is too wide to be due to restoration of the distribution function by Coulomb collisions.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Ion interaction with AEs
In the absence of Coulomb collisions and ICRH the interactions of a resonant ion with an AE lead to a superadiabatic oscillation in the phase space of the invariants of the equation of motion for the drift orbit along the AE characteristics
ΔPφ =nω
ΔW
Δμ=0
If the distribution function increases with energy around the resonance, energy will then be transferred from the ions to the mode and vice verse.
When the distribution function is flattened along all AE characteristics no net transfer of energy takes place. The mode will then be damped by different background damping mechanisms.
P
W
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Decorrelation of the interactions leads to a diffusion of the orbits along the characteristics instead of a superadiabatic oscillation.
Ion cyclotron interactions and Coulomb collisions will partially restore the distribution function in the resonant regions and result in further transfer of energy from the resonant ions to AEs.
The decorrelation of the interactions and local renewal of the distribution function by ICRH increases with energy, whereas they decrease with energy for Coulomb collisions.
Decorrelation of AE interactions and renewal of the distribution function
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Renewal of the distribution function by ICRH
Distribution function f(w) along a characteristic
w
AE resonance
initial distribution function
distribution function flattened by an AE
The width of the resonance and the renewal rate increase with ICRH power
ICRH creates an inverted distribution function along the AE characteristics
High energy ions created by ICRH
Low energy ions removed by ICRH
The dynamics of the AE excitation depend not only on the growth rate of the AE and background damping, but also of the renewal rate of the distribution function and the decorrelation of the wave particle interactions.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
1 LION code L. Villard et al, Computer Physics Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173
Define equilibrium, antenna spectrum, power, type of AE mode etc.
Calculate the dielectric tensor and wave field for ICRH (LION code1) and amplitude of AEs
Calculate changes in orbit invariants by collisions, ICRH and AE with the FIDO code. Remove lost ions, add NBI, -particles and edge source.
Create tables for the various interactions used in the Monte Carlo code with an orbit solver.
Output
The SELFO code calculates the distribution function in the invariant space (W, P, ) with the Monte Carlo code FIDO and the ICRH wave field with the LION code. The AE field can either be calculated with the LION code or from a simplified model.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Monte Carlo code FIDO for calculating the distribution function
W(t+Δt)
Λ(t+Δt)
Pφ(t+Δt)
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
=
W(t)
Λ(t)
Pφ(t)
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ +
μWC
μΛC
μPφC
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ Δt+
AWWC 0 0
0 AΛΛC 0
APφWC APφΛ
C APφPφC
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
ζWC
ζΛC
ζPφC
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
Δt+ωi
∑μWIC
μΛIC
μPφIC
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ Δt+ζW
IC
AWWIC
AΛWIC
APφWIC
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
Δt
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
⎫
⎬ ⎪ ⎪
⎭ ⎪ ⎪
nφ
∑ +
Coulombcollisions ioncyclotroninteractions
+
μWMHD
μΛMHD
μPφMHD
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ Δt+ζW
MHD
AWWMHD
AΛWMHD
APφWMHD
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
Δt
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
⎫
⎬ ⎪ ⎪
⎭ ⎪ ⎪
+.................+.............nφ ,m∑
J. Carlson et al, “Theory of Fusion Plasmas” Varenna 1996, L.-G. Eriksson and P. Helander Phys. Plasmas (1994), T. Bergkvist et al “Theory of Fusion Plasmas” Varenna 2004.
MHD interactions -particle lower ripple sawteething channelling hybrid diffusion
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
TAE Resonance regions
Amplitude variations of the variance of the energy for interactions with an TAE mode. Note that internal zeros of the variance appear.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
The dynamics of TAE and frequency splitting
Fourier decomposition of the time evolution of the mode amplitude gives a characteristic frequency corresponding to the frequency separation of the side bands seen during ICRH.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Mode damping after ICRH switch off
The fast damping of the TAE of about 0.1ms as ICRH is switched off is consistent with experiments.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Conclusions
Self-consistent computations of wave field and distribution function are important for ICRH, in particular for power partition.
The effects of finite orbit width and RF-induced spatial transport are important for many phenomena.
The dynamics of the AEs are strongly affected by ICRH, which have to be taken into account when simulating AE excitation by thermonuclear alpha particles using ICRH ions.
The decorrelation by ICRH increases the width of the resonances and the renewal rate, making the interactions with AE much stronger.
T. Hellsten IEA Burning Plasma Workshop, July 2005 Tarragona Spain
Code for self-consistent modelling of heating
AE
NBI ICRH LH ECRH
Wave field
Power depositionFast ion Fusion reactionsCurrent profileMomentum
Power depositionCurrent profile
Distribution function for electrons f(,W,)3D-Finite element
Source
Ray tracing Ray tracing
Wave spectrum
Wave spectrum
Wave field
Distribution function for ions f(W,P)Monte Carlo method3D-Finite elementMHD
SawteethFishbones
Equi-librium,Loop voltage