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Development of a new reduced model for fast ion transport in TRANSP
M. PodestàM. Gorelenkova, R. B. White,
NSTX-U Energetic Particles Topical Science Groupand NSTX-U Team
NSTX-U Supported by
US TTF 2014San Antonio, TXApril 23rd, 2014
Culham Sci CtrYork U
Chubu UFukui U
Hiroshima UHyogo UKyoto U
Kyushu UKyushu Tokai U
NIFSNiigata UU Tokyo
JAEAInst for Nucl Res, Kiev
Ioffe InstTRINITI
Chonbuk Natl UNFRI
KAISTPOSTECH
Seoul Natl UASIPP
CIEMATFOM Inst DIFFER
ENEA, FrascatiCEA, Cadarache
IPP, JülichIPP, Garching
ASCR, Czech Rep
Coll of Wm & MaryColumbia UCompXGeneral AtomicsFIUINLJohns Hopkins ULANLLLNLLodestarMITLehigh UNova PhotonicsOld DominionORNLPPPLPrinceton UPurdue USNLThink Tank, Inc.UC DavisUC IrvineUCLAUCSDU ColoradoU IllinoisU MarylandU RochesterU TennesseeU TulsaU WashingtonU WisconsinX Science LLC
Supported by DOE contract no. DE-AC02-09CH11466
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
New model introduces selectivity in phase space, generalizes ad-hoc (diffusive) models in TRANSP
• Info on phase space dynamics is of paramount importance for Verification&Validation of codes, theory-experiment comparison
• “Fluid” (integral) quantities do not provide enough information
– Re-computed (“inverted”) Fnb based on measured integral quantities (f.i. density,
neutrons, Er/rotation, NB-driven Jnb, ...) is not unique
>Need details on fast ion energy, pitch and their (consistent) evolution
– E.g. *AE bursts transiently (and selectively) modify phase space; effects propagate during slowing-down
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The new model must be “simple enough” to be included in TRANSP/NUBEAM for routine use reduced model
see M. Podestà et al., PPCF 56 (2014) 055003
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Outline
• New ‘kick model’: basic ideas
• Verification against full ORBIT simulations
• Example from NSTX case w/ TAE avalanche
• Summary
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Outline
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• New ‘kick model’: basic ideas
• Verification against full ORBIT simulations
• Example from NSTX case w/ TAE avalanche
• Summary
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
‘Constants of motion’ are the natural variables to describe resonant wave-particle interaction
Each orbit is fully characterized by:
5
E, energyPz~mRvpar-Y, canonical ang. momentumm~vperp
2/(2B), magnetic moment
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Resonances introduce fundamental constraints on particle’s trajectory in (E,Pz,m)
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From Hamiltonian formulation – single resonance:
w=2pf, mode frequency n, toroidal mode number
Multiple modes, resonances can leadto complicated (DE,DPz) distributions
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
New ‘kick model’ is based on a probability distribution function for particle transport
For each “orbit” in (E,Pz,m), describe steps in DE,DPz by
which can include the effects of multiple modes, resonances: correlated random walk in E, Pz
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In practice, will use the full 5D matrix for p(DE,DPz|Pz,E,m) plus a time-dependent “mode amplitude scaling factor”
3 TAE modes(ORBIT modeling)
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
‘Transport probability’ p(DE,DPz|Pz,E,m) can be computed through numerical codes (e.g. ORBIT) or theory
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- Compute modes, e.g. through NOVA + measurements
- Run ORBIT with Amode=1, constant
- Track (Pz,E,m) in time for each particle, steps dtsim~25-50ms
- Compute steps DE,DPz,Dm
- Re-bin over (Pz,E,m) space
>Obtain p(DE,DPz|Pz,E,m) for each bin in phase space
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Scaling factor Amode(t) is obtained from measurements, or from other observables such as neutron rate + modeling
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- Example: use measured neutron rate- Compute ideal modes through NOVA- Rescale relative amplitudes from
NOVA according to reflectometers- Rescale total amplitude based on
computed neutron drop from ORBIT- Scan mode amplitude w.r.t.
experimental one, Amode=1: get table
- Build Amode(t) from neutrons vs. time, table look-up
- Best option: use experimental data (e.g. reflectometers, ECE)- If no mode data directly available, Amode can be estimated
based on other measured quantities
ORBIT,constant Amode
interpolation
NSTX #139048, t~270ms
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Scheme to advance fast ion variables according to transport probability in NUBEAM module of TRANSP
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NUBEAM step k NUBEAM step k+1
read PlasmaState, Fnb info
convert Fnb(E,p,R,Z)to Fnb(E,Pz,m)
read Amode,p(DE,DPz|E,Pz,m)
convert Fnb(E,Pz,m)to Fnb(E,p,R,Z)
sampleDEj,DPz,j
evolveEj,Pz,j
loop – MC mini-steps
loop – Fnb particles
diagnostics(e.g. classify
orbit)
re-compute sources, scattering, slowing down
add “kicks” to Fnb variables
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Scheme to advance fast ion variables according to transport probability in NUBEAM module of TRANSP
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NUBEAM step k NUBEAM step k+1
read PlasmaState, Fnb info
convert Fnb(E,p,R,Z)to Fnb(E,Pz,m)
read Amode,p(DE,DPz|E,Pz,m)
convert Fnb(E,Pz,m)to Fnb(E,p,R,Z)
add “kicks” to Fnb variables
sampleDEj,DPz,j
evolveEj,Pz,j
loop – MC mini-steps
loop – Fnb particles
diagnostics(e.g. classify
orbit)
re-compute sources, scattering, slowing down,
E,Pz “kicks”
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Outline
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• New ‘kick model’: basic ideas
• Verification against full ORBIT simulations
• Example from NSTX case w/ TAE avalanche
• Summary
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Experimental scenario for initial verification:NSTX H-mode plasma with bursts of TAE activity
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E. Fredrickson et al., Nucl. Fusion 2013
TAE Avalanches:
Focus on this event
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Evolve Fnb from NUBEAM assuming fixed background, compare with ORBIT
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Fnb(E,Pz,m) from NUBEAM
read Amode,p(DE,DPz|E,Pz,m)
convert Fnb(E,Pz,m)to Fnb(E,p,R,Z)
sampleDEj,DPz,j
evolveEj,Pz,j
loop – MC mini-steps
loop – Fnb particles
diagnostics(e.g. classify
orbit)
add “kicks” to Fnb variables
Verify agreement for :–Single particle orbits–Whole ensemble of particles (preserve statistics)–Global quantities: density profile
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Change in orbit type observed for some particles:fast ions are kicked around in phase space by TAEs
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blue: initial orbitred: final orbit
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Good agreement with ORBIT is preserved when evolving Fnb over 5 ms, typical macro-step of NUBEAM
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• Similar results for Pz • Satisfactory reconstruction over ~3 orders of magnitude for
co-, trapped (, counter- not present in this input Fnb) particles
black: ORBIT red: Kick Model r: correlation coefficient error: (ORBIT-model)/ORBIT
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Fnb after 5ms shows fast ion redistribution, only modest losses; NB driven “current” also affected.
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- Compare full ORBIT simulation with reconstructions from reduced model
- Fnb drops in the core, fast ions redistributed to larger radii
- Define rough proxy for NB-driven (parallel) current, Inb~Fnb p v
- Larger (relative) variations for Inb than for Fnb in the core
> Need NUBEAM/TRANSP for more quantitative calculations of Inb
solid: modeldashed: ORBIT
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Outline
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• New ‘kick model’: basic ideas
• Verification against full ORBIT simulations
• Example from NSTX case w/ TAE avalanche
• Summary
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Next step: use stand-alone NUBEAM and IDL scripts to simulate Fnb evolution for >>5 ms
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NUBEAM step k NUBEAM step k+1
read PlasmaState, Fnb info
convert Fnb(E,p,R,Z)to Fnb(E,Pz,m)
read Amode,p(DE,DPz|E,Pz,m)
convert Fnb(E,Pz,m)to Fnb(E,p,R,Z)
add “kicks” to Fnb variables
sampleDEj,DPz,j
evolveEj,Pz,j
loop – MC mini-steps
loop – Fnb particles
diagnostics(e.g. classify
orbit)
re-compute sources, scattering, slowing down
after “kicks”
IDL scripts
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Reduced model reproduces neutron evolutionfor nominal Amode(t) from neutrons, Mirnovs
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- Initial comparison of model predictions w/ experimental neutron rate
- Use stand-alone version of NUBEAM, iterate with reduced model (IDL scripts)
- Background plasma is fixed- Normalize exp. neutron rate to
central ion density vs. time- Normalize all neutron rates at
t=267 ms (before first burst)
Satisfactory agreement for Amode(t) from neutron rate, Mirnovs
model
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Reduced model + NUBEAM reproduces fast ion redistribution; NB-driven current strongly affected, too
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- Initial tests show fast ion redistribution induced by each TAE avalanche
- Clear effects on NB-driven current, Jnb
- Stronger effect than on Fnb
- AE effects persist on slowing down time scales
- Constant NB injection counteracts Fnb, Jnb depletion
267 ms271 ms279 ms
solid: classical w/ AFIDdashed: w/ MHD
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Clear resonance patterns seen on Fnb modified through kick model – not seen in “standard” TRANSP
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Relative variation (Fnb,1-Fnb,0)/Fnb,0 , t=265-275ms
TRANSP w/ AFID kick model
– Resonances appear as localized in energy, pitch
– Simple diffusion not adequate to reproduce this
– Will enable more direct comparison with measurements sensitive to phase space modifications
[Heidbrink, RSI 2010]Example: weight function for FIDA measurements
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
The model has been recently improved to account for multiple “classes” of modes in same discharge
Quite common scenario:
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> Each “class” is modeled by pk(DE,DPz), weighted by Amode,k– Total kicks result from Sk Amode,k(t) x pk(DE,DPz)
>Provides more realistic Fnb evolution when modes have comparable amplitude
>Account for differences in equilibrium, modes at different stages of the discharge
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Preliminary example: NSTX scenarios with simultaneous TAEs and kink-like modes
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TAEs + kink-like: - Anomalous diffusivity (AFID) up
to t=320ms to match neutrons
- Set AFID=0 after 320ms
- Keep profiles fixed
- Use p1(DE,DPz) for TAEs, same as for avalanches
- Use p2(DE,DPz) for kink-like modes- Crude model w/ n=1,2,3- Just a test case!
> Analysis in progress to obtain “real” kink structure
w/ AFID
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Outline
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• New ‘kick model’: basic ideas
• Verification against full ORBIT simulations
• Example from NSTX case w/ TAE avalanche
• Summary
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Summary
• Test algorithm for reduced fast ion transport model developed, being verified– Results compared with full ORBIT runs– Confirmed validity of approach for practical case
• Successful preliminary tests for NSTX case with TAE modes (avalanches)– Shot#139048, t~265-320 ms: H-mode avalanches– Strong redistribution (energy, radius) of fast ions inferred– Modest losses, consistent with previous detailed modeling– NB-driven current Jnb is strongly perturbed
> Implementation in NUBEAM under way> Extensive Verification & Validation planned (multi-machine,
multi-mode)> Identify issues, possible improvements to the model
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more details: M. Podestà et al., PPCF 56 (2014) 055003
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Backup
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Four models are presently implemented in TRANSP for fast ion diffusion/convection coefficients, Db & vb
All have diffusive/convective nature in radial coordinate; little/no phase space selectivity:
1)
2)
3)
4)
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[from http://w3.pppl.gov/~pshare/help/transp.htm]
kADIFB : multiplierDe(x,t) : electron particle diffusivity
DeWP(x,t) : electron particle
diffusivity from Ware-pinch corrected flux
Dk(E,x,t): diffusivity for deeply trapped, barely trapped, co- barely passing, ...
diffusion/convection model
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
For low-frequency *AEs with w<<wci such as TAEs, magnetic moment m is conserved (...but maybe it’s not)
• In this presentation, it is assumed that Dm=0
• However: Dm=0 hypothesis can break down if– rf ~ radial width of the modes– rf ~ scale-length of equilibrium profiles➮ Both conditions are likely to be met in spherical tokamaks (e.g. NSTX)
➮ Proposed model can be generalized to cases where m is not conserved– Also important for wci-range instabilities: GAE/CAEs
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Example for single-resonance case:analytical probability distribution function
For each bin in (E,Pz,m), steps in DE,DPz are approximated by a bivariate
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DPz
DE
~n/w
normalization
correlation parameter,
such that
...and all parameters depend, in principle, on the mode amplitude A=A(t)
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Single (isolated) resonances introduce fundamental constraints on particle’s trajectory in (E,Pz,m)
• From Hamiltonian formulation:
w=2pf, mode frequency n, toroidal mode number
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Presence of multiple modes/resonances distortsthe ‘ideal’ (linear) relationship
4 TAE modes,“large” amplitude:- broadening- multiple n/w’s
(from ORBIT simulation)
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
An analytical formulation for p(DE,DPz|Pz,E,m) could be developed – but it would be quite unpractical
E.g., use:
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In practice, will use the full 5D matrix for p(DE,DPz|Pz,E,m)
1 TAE, large amplitude 4 TAEs, small amplitude
2 TAEs, A1 A≃ 2, w2<0 no TAEs, large (unphysical) nscattering
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
NSTX, TAE avalanche
Mode amplitude can evolve on time-scales shorter than typical TRANSP/NUBEAM steps of ~5-10 ms
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Fnb evolution must be computed as a sequence of sub-steps
– Duration dtstep sufficiently shorter than time-scale of mode evolution
– Examples here have dtstep~25-50 ms
Energy and Pz steps assumed to scale linearly with mode amplitude
– Roughly consistent with ORBIT simulations
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Example: Amode(t) computed from measuredneutron rate or Mirnov coils’ signal
Get A(t) from measured neutrons+table look-up:
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- Compute fractional Rn drops vs. time
- Use table Rn vs Amode to find corresponding (normalized) mode amplitude
Mirnovs
neutrons
- Comparison w/ Amode(t) from Mirnov coils
- Do different waveforms lead to differences in fast ion evolution? Not on relevant time scales > 1ms
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Scheme to advance fast ion variables according to transport probability in NUBEAM module of TRANSP
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NUBEAM step k NUBEAM step k+1
read PlasmaState, Fnb info
convert Fnb(E,p,R,Z)to Fnb(E,Pz,m)
read Amode,p(DE,DPz|E,Pz,m)
convert Fnb(E,Pz,m)to Fnb(E,p,R,Z)
sampleDEj,DPz,j
evolveEj,Pz,j
loop – MC mini-steps
loop – Fnb particles
diagnostics(e.g. classify
orbit)
re-compute sources, scattering, slowing down
after “kicks”
add “kicks” to Fnb variables
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Scheme to evolve Fnb takes into account (in a semi-empirical way) constraints of resonant interaction
• Particle’s motion is characterized by different time-scales:– Fast oscillation in wave field – neglected– ‘Jumps’ DE,DPz around instantaneous energy, Pz
– Slow (secular) drift from initial energy, Pz
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lost
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Putting all together
At each ‘macroscopic’ NUBEAM step:I. Re-normalize bins (Pz,E,m) based on q-profile, fields, ...II. Identify ‘bin’ in (Pz,E,m) for current ‘particle’ (i.e. orbit)III. Extract steps sE,sPz (sm) from multivariate p(DE,DPz,Dm)IV. Compute sign Sr,i from p(DE,DPz): positive or negative kicksV. Rescale steps based on Amodes(t)
VI. Advance E, Pz (m):
VII. Advance particle’s trajectory in phase space for next stepVIII. Compute slowing down, scattering (NUBEAM)
where steps II-VII are divided in sub-steps for each particle
Required input, e.g. through ‘Ufiles’:scaling factor (“mode amplitude”) Amode, probability p(DE,DPz) 37
Loop
ove
r par
ticle
s
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Discrete bins in (Pz,E,m) can contain both resonantand non-resonant particles
• ‘Non-resonant’ particles have small fluctuations around initial (E, Pz)
• ‘Resonant’ particles can experience large DE, DPz variations
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• To keep track of particle’s class:– Sample steps sE, sPz at first step only– This mimic the “correlated random walk” experienced by the particles– Exception: particle move to a different bin -> re-sample
p(DE,DPz)
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
p(DE,DPz|Pz,E,m) can be skewed to positive/negative DE,DPz, causing overall “drift” of Fnb(Pz,E,m)
• Introduce ‘random sign’ for i-th step in MC procedure, Sr,i
• For each particle (e.g. pair of correlated steps sE, sPz), calculate Sr,i from probability of positive vs. negative steps
– From p(DE,DPz) compute
– Then define fsign:
– Finally, use 0<fsign<1 to bias random extraction of Sr,i=+1,-139
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Only a few particles (~0.1%) are actually lost for the cases examined here; redistribution dominates
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blue/green: initial orbitsred/yellow: final orbits
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Example: evolving Fnb over 270 ms in 5 sub-steps
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black: ORBIT
red: Model
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Reconstruction works for different classes:co-, counter-, trapped
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black: ORBIT
red: Model
co-passing counter-passing trapped
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Reconstruction works at different sub-steps
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black: ORBIT red: Model
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Good agreement with ORBIT is preserved when evolving Fnb over 5 ms, typical macro-step of NUBEAM
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Satisfactory reconstruction over 3 orders of magnitude forco-, trapped (, counter- not present in this input Fnb) particles
r: correlation coefficienterror: (ORBIT-model)/ORBIT
black: ORBIT
red: Kick Model
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Tests assuming different mode amplitudes are satisfactory, though not perfect...
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• Reconstruction vs. amplitude is satisfactory
black: ORBITred: Kick Model
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Tests assuming different mode amplitudes are satisfactory, though not perfect...
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black: ORBITred: Kick Model
• Reconstruction vs. amplitude is satisfactory• Differences ascribed to simplifications in p(DE,DPz) scaling
with Amode: shape does change
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Results are sensitive to input mode amplitude; time steps must be chosen to satisfy “statistical” approach
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- Typical time scales:- Slowing down: 15-30ms- Collisions: 2-5ms- AEs: 0.1-2ms
Amode(t) from neutron rate
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Results are sensitive to input mode amplitude; time steps must be chosen to satisfy “statistical” approach
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- Typical time scales:- Slowing down: 15-30ms- Collisions: 2-5ms- AEs: 0.1-2ms
- N: number of micro-steps for MC particle evolution, duration 25ms
Amode(t) from neutron rate
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Sensitivity study suggests fast ion density is good candidate for thorough model-experiment comparison
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neutron rate / reference fast ion density / reference
Neutrons:- Mostly indicative of high-energy fast ions- Limited/no information on other portions of phase
space
Density:- All energies matter; more sensitive- Accessible through FIDA, NPA diagnostics w/
spectral information
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Summary of sensitivity study – neutron rate
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Summary of sensitivity study – beam ion density
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Preliminary example: NSTX scenarios with simultaneous TAEs and kink-like modes
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Baseline: - Anomalous diffusivity (AFID) up
to t=320ms to match neutrons
- Set AFID=0 after 320ms
- Keep profiles fixed
AFID AFID=0, use new model
new model
TRANSP w/ AFID
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Preliminary example: NSTX scenarios with simultaneous TAEs and kink-like modes
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TAEs + kink-like: - Anomalous diffusivity (AFID) up
to t=320ms to match neutrons
- Set AFID=0 after 320ms
- Keep profiles fixed
- Use previous p1(DE,DPz) for TAEs
- Use p2(DE,DPz) for kink-like modes- Crude model w/ n=1,2,3- Just a test case!
- Analysis in progress to obtain “real” kink structure
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Preliminary example: NSTX scenarios with simultaneous TAEs and kink-like modes
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TAEs + kink-like: - Anomalous diffusivity (AFID) up
to t=320ms to match neutrons
- Set AFID=0 after 320ms
- Keep profiles fixed
- Use previous p1(DE,DPz) for TAEs
- Use p2(DE,DPz) for kink-like modes- Crude model w/ n=1,2,3- Just a test case!
- Analysis in progress to obtain “real” kink structure
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Preliminary example: NSTX scenarios with simultaneous TAEs and kink-like modes
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- Multi-mode case can account for (some type of) synergy between different modes
kink-like,finite freq.
TAEs
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NSTX-U Reduced model for fast ion transport in TRANSP - M. Podestà (TTF 2014)
Can the model be used in predictive mode?
• As it is, the model is OK to analyze ‘real’ discharges– Need mode structure to calculate p(DE,DPz), e.g. from NOVA-K and
reflectometers’ data + ORBIT– Need data (Mirnovs, neutrons, etc.) to infer Amodes(t)
• Two possibilities for ‘predictive’ runs:– Find reasonable guess for unstable modes (e.g. NOVA-K)– Explore different scenarios w/ scan of Amodes(t): weak *AE activity,
bursts/avalanches, etc.or:– Have an additional module to compute Amodes(t) self-consistently?– Still requires mode structure, probably estimates for gdrive, gdamp
– Let Amodes(t) evolve according to Fnb evolution – but how?– Couple to other reduced models, e.g. Critical Gradient Model?
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