HAGIS Code
Lynton Appel
… on behalf of Simon Pinches
and the HAGIS users
EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon, UK
CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority
HAGIS Description1
• Self-consistently models the nonlinear interaction between
spectrum of linear eigenfunctions and fast particle distribution
function
– Weakly damped global Alfvén Eigenmodes (AE) could be driven unstable
by fusion-born -particles
•
Straight field-line equilibrium
–
Boozer coordinates
•
Hamiltonian description of particle motion
•
Fast ion distribution function
–
•
f method
Evolution of waves
–
1SD
Wave eigenfunctions computed by
CASTOR/MISHKA/CAS-3D and held
invariant throughout system evolution
Pinches, LC Appel et al., Comput. Phys. Commun. 111 131 (1998)
The HAGIS code -
ANU, Australia
May 2010
Boozer Coordinates
The HAGIS code -
ANU, Australia
May 2010
Evolution of Energetic Particles
The HAGIS code -
ANU, Australia
May 2010
Equations of Motion
• Derived from total system Hamiltonian
The HAGIS code -
ANU, Australia
May 2010
Fast Particle Orbits
• ICRH ions in JET deep shear
reversal
– On axis heating:
 = B0/E = 1
z [m]
– E = 500 keV
R [m]
The HAGIS code -
ANU, Australia
May 2010
Calculation of AE Eigenfunctions
The HAGIS code -
ANU, Australia
May 2010
Wave Evolution
The HAGIS code -
ANU, Australia
May 2010
Wave Equations
• Linear eigenstructure assumed invariant
• Introduce slowly varying amplitude and phase:
• Gives wave equations as:
Additional mode
damping rate, d
• where
The HAGIS code -
ANU, Australia
May 2010
Delta f Method
- νeff δf
The HAGIS code -
ANU, Australia
May 2010
Quiet Start Method
The HAGIS code -
ANU, Australia
May 2010
Conservation of Particles
The HAGIS code -
ANU, Australia
May 2010
Applications
• AE linear growthrates and
nonlinear saturation amplitudes
Mode saturates
at B/B~10-3
np =
52,500
• Determination of
– fast particle re-distribution
– Fast particle losses
d/0=2.7%
Fast ion
redistribution
Waveparticle
trapping
The HAGIS code -
ANU, Australia
May 2010
TAE Amplitude Determination
•
Frequency [kHz]
•
Frequency sweeping observed
when damping rate ~ linear
growth rate and holes/clumps
form in particle phase space
Modelling with HAGIS allows
determination of experimental
internal mode amplitudes from
observed frequency sweeping
Particle trapping frequency
determined using HAGIS
Chirping modes exhibit
frequency sweeping,
/0~ 20%
MAST #5568
120
100
80
64
66
68
70
72
Time [ms]
1.2
Frequency [0]
•
140
1.1
1.0
0.9
0.8
0.7
0
50
100
Time [Lt]
The HAGIS code -
ANU, Australia
May 2010
150
Fast Ions in MAST
• High performance MAST plasmas
achieved with off-axis NBI
– Off-axis NBI current drive used to
tailor current profile
• Fast ion distribution very different
with on and off axis injection
– Changes to current profile with offaxis beams studied in MAST
The HAGIS code -
ANU, Australia
May 2010
Transport Code Modelling
• Discrepancy in neutron
rate coincident with
observation of fast
particle driven modes
Sn
TRANSP
Experiment
Difference
– Fishbones
• Can be explained by
introducing an
anomalous fast ion
diffusion, D~0.5 m2/s
The HAGIS code -
ANU, Australia
May 2010
Fast Particle Simulations
• Fishbones simulated in HAGIS to study effect on fast ion
population and calculate an effective fast ion diffusion
The HAGIS code -
ANU, Australia
May 2010
Comparison with Experiment
• Levels of anomalous fast ion
diffusion found in simulations
consistent with those required in
transport codes to explain
observations:
– Neutron rate
– Stored energy
– Current profile
The HAGIS code -
ANU, Australia
May 2010
HAGIS code performance
6000
1/n scaling
5000
Run time [s]
Linux Cluster
4000
Wall clock time
to calculate
TAE linear
growthrate in
ITER
3000
2000
1000
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Number of processors, #
• HAGIS code parallelises very well
– relatively low level of inter-processor communication traffic
The HAGIS code -
ANU, Australia
May 2010
14