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Journal Article•DOI•

A comparison of the impact of central ECRH and central ICRH on the tungsten behaviour in ASDEX Upgrade H-mode plasmas

C. Angioni1, M. Sertoli1, R. Bilato1, V. Bobkov1, A. Loarte2, R. Ochoukov1, T. Odstrcil1, Th. Pütterich1, J. Stober1 •
Max Planck Society1, ITER2
24 Mar 2017-Nuclear Fusion (IOP Publishing; IAEA)-Vol. 57, Iss: 5, pp 056015
TL;DR: In this paper, a comparison of the impact of additional central electron cyclotron resonance heating (ECRH) and ICRH on the behavior of the tungsten (W) density in the core of H-mode plasmas heated with neutral beam injection (NBI) is performed in ASDEX Upgrade.
Abstract: A comparison of the impact of additional central electron cyclotron resonance heating (ECRH) and ion cyclotron resonance heating (ICRH) on the behaviour of the tungsten (W) density in the core of H-mode plasmas heated with neutral beam injection (NBI) is performed in ASDEX Upgrade. Both localized and broad profiles of the power density of the ECRH have been obtained, where broad profiles reproduce the profile shape of the ICRH power density, which is applied with a hydrogen minority heating scheme. In contrast to ECRH, which produces direct electron heating only, ICRH eventually heats both electrons and ions in almost equal fractions. It is found that both additional RF heating systems reduce the peaking of the W density profile with increasing central RF heating power. Approximately the same values of W density peaking are obtained when the same values of electron heating are produced by the two RF heating systems, which implies that less total heating power is required with ECRH than with ICRH to reduce the W density peaking. A related modelling activity shows that an important ingredient to explain the experimentally observed trend is the variation of the turbulent W diffusion as a function of the electron to ion heat flux ratio. Additional effects are connected with the more favorable W neoclassical transport convection in the presence of ICRH, produced by the combination of stronger central ion temperature gradients and the impact of the H minority on the W poloidal density asymmetry.

Summary (2 min read)

Jump to: [1. Introduction] – [2. Experimental investigation of the W response to central ECRH and] – [3. Modelling of the experimental results] and [4. Conclusions]

1. Introduction

  • Central RF heating not only modifies the temperature, density and rotation profiles of the main plasma, but can also directly modify the impurity transport.
  • In order to identify the transport mechanisms which can explain the new observations reported in this paper, power density profiles of ECRH and ICRH have been computed with the codes TORBEAM [45] and TORIC–SSFPQL [46], and complete power balance calculations have been obtained with TRANSP [47].
  • In Section 2 the experiment is described and the experimental results are presented.
  • In section 3 the observations are modelled in order to shed light on the relative role of the transport mechanisms governing the W density behaviour.

2. Experimental investigation of the W response to central ECRH and

  • ICRH ICRH is applied with a H-minority heating scheme, with a H concentration around 5%, with both the 2–straps antenna with boron coated limiters and the 3–straps antenna with tungsten coated limiters [53].
  • An interesting observation is that, during the power steps with relatively low levels of RF heating, the W behaviour can reach stationary conditions with a W density profile which is significantly more peaked than the electron density profile.
  • The authors observe that plasmas with additional ICRH heating exhibit higher values of R/LT i and lower values of Te/Ti than cases with additional ECRH, consistent with an increased level of ion heating in the center produced by ICRH.
  • Similar to the observations reported in [34], also in the heating phases examined in the present work, sawteeth are present and are characterized by the occurrence of (1, 1) modes, which appear early after the sawtooth crash and saturate over a large portion of the sawtooth period.

3. Modelling of the experimental results

  • In this section the experimental results are examined with both simplified models and theoretical models in order to identify the main ingredients which are required to reproduce the experimental trends.
  • In particular, the drift–kinetic code NEO [48–50] and the gyro–kinetic code GKW [51,52] are applied to compute the neoclassical and the turbulent W transport components using as inputs the measured profiles of the main plasma (deuterons and electrons).
  • The authors also notice that neoclassical transport only (case with Dturb/χeff = 0) predicts too large peaking factors for most of the ECRH cases, whereas values of Dturb/χeff ≥ 1 are inconsistent with the observed accumulation at the lowest values of Qe/Qtot.
  • At high additional RF heating powers, the neoclassical diffusion coefficient is smaller than the turbulent diffusion coefficient.
  • The results of the combined NEO and GKW modelling are presented in Fig. 11, where predicted flux–surface–averaged density profiles are compared with those reconstructed from the experimental measurements, and in 12, where the predicted central peaking factor parameter is compared to the corresponding experimental results as a function of the fraction of electron heat flux.

4. Conclusions

  • Experiments in AUG have been performed to directly compare the impact of central ECRH and central ICRH on the W behaviour.
  • In these experiments both ECRH and ICRH have been applied in addition to a background of NBI heating, which is mainly delivering ion heating in the central region of the plasma.
  • The absence of strong central NBI heating in an ITER plasma has some positive consequences with respect to the W behaviour.

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A comparison of the impact of central ECRH and
central ICRH on the tungsten behaviour in ASDEX
Upgrade H-mode plasmas
C. Angioni
1
, M. Sertoli
1
, R. Bilato
1
, V. Bobkov
1
, A. Loarte
2
, R.
Ochoukov
1
, T. Odstrcil
1
, T. P¨utterich
1
, J. Stober
1
and the
ASDEX Upgrade Team
1
Max-Planck Institut f¨ur Plasmaphysik, Garching, Germany
2
ITER Organization, Route de Vinon-sur- Verdon, CS 90 046, 13067 St Paul Lez
Durance, France
Abstract. A comparison of the impact of additional central ele ctron cyclotron
resonance heating (ECRH) and ion cyclotron r e sonance heating (ICRH) on the
behaviour of the tungsten (W) density in the core of H-mode plasmas heated with
neutral beam injection (NBI) is performed in ASDEX Upgrade. Both localized and
broad profiles of the power density of the ECRH have b een obtained, where broa d
profiles reproduce the profile shape of the ICRH power density, which is applied with
a hydrogen minor ity heating scheme. In contrast to ECRH, which produces direct
electron heating only, ICRH eventually hea ts both electrons a nd ions in almost equal
fractions. It is found that both additional RF heating systems re duce the peaking
of the W density pro file with increasing central RF heating power. Approximately
the sa me values of W density peaking are obtained when the same values of electr on
heating are produced by the two RF heating systems, which implies that less total
heating power is required with ECRH than with ICRH to reduce the W density
peaking. A related modelling activity shows that an important ingr e die nt to explain
the e xp erimentally observed trend is the variation of the turbulent W diffusion as a
function of the electron to ion heat flux ratio. Additional effects are connected with the
more favorable W neoclassical transport convection in the presence of ICRH, produced
by the combination of stronger central ion temperature gradients and the impact of
the H minority on the W poloidal density asymmetry.
PACS numbers: 52.55.Fa, 52.25.Fi, 52.25.Vy, 52.65.Tt
A comparison of the impact of central ECRH and central ICRH on the tungsten behaviour in ASDEX Upgr
1. Introduction
Heavy impurities are expected to play a critical role in a fusion reactor plasma, not only
because tungsten (W, Z = 74, A = 184) is currently considered as a first wall material,
but also because highly charged impurities are planned t o be seeded in order to radiate
part of the heating power in the plasma p eriphery and reduce the power loads directly
reaching the walls. Thereby, r obust methods by which the impurity concent ration a nd
the shape of the impurity density profile can be kept under control have to be identified.
These are determined by the combination of the effects of the peripheral sources and the
transport fro m the scrape-off-layer to the plasma core. Central radio frequency (RF)
heating has b een ident ified as a reliable method to limit the central concentration of
heavy impurities [1–9]. Since the behaviour and the profile shapes of heavy impurities
are determined by both turbulent [10–23] and neoclassical transport [25–30], and are also
affected by the presence of magneto-hydrodynamic (MHD) instabilities [6, 31–35], the
physics behind the reduction of the central peaking of the W density produced by central
RF heating can be expected to involve a certain level of complexity, in which multiple
effects are combined. Central RF heating not only modifies the tempera t ur e, density
and rotation profiles of the main plasma, but can also directly modify the impurity
transport. Central accumulation (that is, a W density profile centrally more peaked
than the electron density profile) is produced by the dominance of neoclassical transport
in the unfavourable conditions of inward neoclassical convection (pinch) [1,2,33,36–44].
Turbulent t ransport is not predicted to lead to strong central accumulation (e.g. [13])
and thereby an increase of turbulent impurity transport can offset the neoclassical
pinch. Finally, central RF heating can modify the characteristics of MHD instabilities,
particularly at the q = 1 surface, with impact on the impurity behavior [6, 31, 32, 34].
Here we repo r t the results obtained in an experiment at ASDEX Upgrade ( AUG) in
which plasma discharges have been performed in order to compare the impact of central
electron cyclotron resonance heating (ECRH) and ion cyclotron resonance heating
(ICRH), where the latter is applied with a H–minority heating scheme. D ecreasing
steps of RF heating power have been added to a ba ckground o f neutral beam injection
(NBI) heating power during the current flat–top phase of the plasma discharges, with the
plasma in the H–mode confinement regime. Both localized and broad power deposition
profiles of the ECRH have been produced, where the broad profile reproduces the power
deposition profile shape produced by central ICRH. The experimental results confirm
the beneficial role of cent r al RF heating in reducing the central peaking of the W density,
consistent with previous studies. In addition they allow a direct comparison of the two
RF heating methods and reveal that comparable effects on the W density are produced
when similar amounts of additional electron heating are delivered to the plasma. This
observation implies that, at least in these conditions with a background of large NBI
heating, ECRH is more efficient in reducing the peaking of t he W density, since it
delivers all of the power to the electrons, whereas, with the heating scheme applied in
these experiments, ICRH also has a fr action of the power which heats the ions. The
critical role of electron heating in flattening the central density profile of heavy impurities
A comparison of the impact of central ECRH and central ICRH on the tungsten behaviour in ASDEX Upgr
revealed by these experiments appears to be consistent with previous results at JET [4],
where nickel (Ni) density profiles were observed to be flat with central ICRH in mode
conversion, producing dominant electron heating, and p eaked with central ICRH in He
3
minority heating scheme, producing dominant ion heating, although also with different
power deposition profiles. Moreover, higher values of the cent ral diffusion coefficient of
silicon (Si) were measured in ASDEX Upgrade with central ECRH in comparison to
central ICRH [2], although also in this case the power deposition profiles of ECRH were
more centrally localized than those of ICRH.
In order to identify the transport mechanisms which can explain the new
observations reported in this pap er, power density profiles of ECRH and ICRH have been
computed with the codes TORBEAM [45] and TORIC–SSFPQL [46], and complete
power balance calculations have been obtained with TRANSP [47 ]. In addition,
exp erimentally reconstructed profiles of the W density are compared with the predictions
obtained by combining the results of codes which separately compute neoclassical
and turbulent transport, drift–kinetic NEO [48–50] and gyro–kinetic GKW [51, 52]
respectively. The modelling activity is particularly devoted to identify reasons which can
at least partly explain the observed positive role of electron heating produced by the RF
heating systems. We also note tha t these codes have been run assuming axisymmetric
geometry, that is in the absence of any perturbation of the confining magnetic field
produced by MHD modes.
In Section 2 the experiment is described and the experimental results are presented.
In section 3 the observations are modelled in or der t o shed light on the relative role of
the t r ansport mechanisms governing the W density behaviour. Finally in Section 4
conclusions are drawn.
2. Experimental investigation of the W response to central ECRH and
ICRH
In o rder t o compare the impact of central ECRH and centra l ICRH on W transport in
otherwise similar conditions, plasma discharges of 1 MA and magnetic field around 2.5 T
(q
95
≃ 4) have been produced in ASDEX Upgrade at the line averaged electron density of
n
e
= 7.2 10
19
m
−3
, with the current fla t top phase in the H-mode confinement regime,
heated by 7.5 MW of constant NBI heating power and by decreasing power steps of
central ECRH (from 1.9 MW to 0.2 MW) and ICRH (from 3.6 MW to 0.2 MW). ICRH
is applied with a H-minority heating scheme, with a H concentration around 5%, with
both the 2–straps antenna with boron coated limiters and the 3–straps antenna with
tungsten coated limiters [53]. 3 gyrotrons at 1 40 GHz [54] have been used for ECRH.
Intermediate power steps of ECRH are o bt ained by modulation of the power at the high
frequency of 150 Hz and with 50% duty cycle for each gyrotron. Time traces of two
discharges with decreasing power steps of ICRH and ECRH are presented in Fig. 1 and
Fig. 2 respectively. With decreasing RF power (Figs. 1b and 2b), the W concentration
at the center (Figs. 1c and 2c) (obtained from a fit of the spectrum around 5nm
measured on a single centr al line-o f-sight by the grazing incidence spectrometer ( GIW))
A comparison of the impact of central ECRH and central ICRH on the tungsten behaviour in ASDEX Upgr
0
2
4
6
8
P
NBI
P
rad
[MW]
(a)
0
2
4
[MW]
P
ECH
P
ICRH
(b)
2 4 6 8
10
−5
10
−4
10
−3
ρ ~ 0.1
ρ ~ 0.5
c
W
(c)
0
1
2
[10
20
m
3
]
n
e 20
f
ELM
[100 Hz]
(d)
2 4 6 8
0
1
2
[MJ]
time [s]
β
N
W
MHD
(e)
Figure 1. Time traces of AUG shot ♯324 04 with decreasing steps of ICRH power,
total NBI and radiated powers (a), total ECH and ICRH powers (b), W concentration
c
W
= n
W
/n
e
at ρ ≃ 0.1 and ρ ≃ 0.5 (c), ELM frequency and line averaged density
(d), normalized β and total stored energy (e).
0
2
4
6
8
P
NBI
P
rad
[MW]
(a)
0
1
2
[MW]
P
ECH
(b)
2 4 6 8
10
−5
10
−4
10
−3
ρ ~ 0.1
ρ ~ 0.5
c
W
(c)
0
1
2
[10
20
m
3
]
n
e 20
f
ELM
[100 Hz]
(d)
2 4 6 8
0
1
2
[MJ]
time [s]
β
N
W
MHD
(e)
Figure 2. Time traces of AUG shot ♯32408 with decreasing steps of ECRH p ower,
total NBI and radiated powers (a), total ECH and ICRH powers (b), W concentration
c
W
= n
W
/n
e
at ρ ≃ 0.1 and ρ ≃ 0.5 (c), ELM frequency and line averaged density
(d), normalized β and total stored energy (e).
A comparison of the impact of central ECRH and central ICRH on the tungsten behaviour in ASDEX Upgr
progressively increases, eventually leading to central accumulation, as also shown by the
corresponding fast increase of the total radiated power (Figs. 1a a nd 2a). The level of
gas puff, by which the ELM frequency can be regulated and the W concentration at
the pedestal top can be limited, is kept to low values in these discharges, and sudden
uncontrolled W accumulation is o bserved in the presence of NBI heating only (usual in
ASDEX Upg r ade H-modes at high plasma currents [3]) .
An interesting observation is that, during the power steps with relatively low levels
of RF heating, the W behaviour can reach stationary conditions with a W density profile
which is significantly more peaked than the electron density profile. Thereby, strictly
speaking, W accumulation is observed, but this does not lead to an uncont rolled process
of increasing accumulation, which instead suddenly takes place in conditions of NBI only
heating, as shown for instance in F igs. 1 and 2. This property is illustrated in Fig. 3
where the time evolutions of the flux–surface–averaged W density profiles (reconstructed
by a SXR W density diagnostic [55]) are plotted as a function of normalized minor radius
r/a and time during high (a,d) and low (b,e) a dditional RF power phases of the two
discharges with additional ICRH (a,b) and ECRH (d,f), whose time traces were already
presented in Figs. 1 and 2 respectively. In Fig. 3 (a,b,d,e), the oscillations of the W
density are produced by sawteeth. In Fig. 3 ( c,e), the time averaged W density profiles
are compared to the corresponding electron density profiles. The profiles are nor ma lized
to their values at r/a = 0.4 (that is, all of the normalized profiles cross 1 at r/a = 0.4).
Fig. 3(c,e) demonstrate that in phases with high RF power no accumulation ta kes pla ce,
whereas in phases with low RF power, statio nary conditions are achieved which exhibit
significant W accumulation.
Since in AUG the ICRH power deposition profiles are relatively broad as compared
to the possibilities of the ECRH power, dischar ges with decreasing power steps of ECRH
have been applied with 3 gyrotrons all converging to a deposition close t o the magnetic
axis (ρ
dep
≃ 0.1) as well as with 3 gyrotrons aiming at different radial locations in
order to approximatively reproduce the profile of the deposited power from ICRH (as
obtained by TORIC–SSFPQL [46] simulations applied to a previous similar plasma).
A compar ison of the profiles of the deposited power with localized ECRH, with broad
ECRH, (computed by TORBEAM [45]) as well as with ICRH (computed with TORIC–
SSFPQL [46]) a re presented in Fig. 4. We also observe that, in comparison with the
RF power profiles, the power density and heat flux profiles produced by NBI (computed
with TRANSP [47]) are much broader than the corresponding profiles produced by the
RF heating systems (4 a,b). However, considering the actual levels of the heat fluxes
in MW (4 c), in the central region the NBI heat flux is comparable to that of broad
ECRH at the maximum p ower step (1.9 MW), whereas the ICRH heat flux profile at
the maximum power step of 3 .4 MW is closer to that obtained with localized ECRH at
1.9 MW. In these discharges, in almost the totality of the heating phases, sawteeth are
present, with sawtooth periods of the order of 100 ms a nd sawtooth inversion radius
usually located between r/a = 0.3 and r/a = 0.35. In the analysis we consider pr ofiles
which are averaged over time windows of about 500 ms, which contain multiple sawtooth
cycles and which provide averaged profiles over the sawtooth oscillations. We o bserve
Citations
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Poloidal variation of high-Z impurity density due to hydrogen minority ion cyclotron resonance heating on Alcator C-Mod

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Cites background from "A comparison of the impact of centr..."

  • ...In addition, the role of neoclassical W transport in the core is expected to be much smaller in a reactor plasma compared to current devices, resulting in less charge-dependent inward directed convective transport [46]....

    [...]

Journal Article•DOI•
Parametric dependencies of the experimental tungsten transport coefficients in ICRH and ECRH assisted ASDEX Upgrade H-modes

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Abstract: The profiles of the W transport coefficients have been experimentally calculated for a large database of identical ASDEX Upgrade H-mode discharges where only the radio-frequency (RF) power characteristics have been varied [Angioni et al., Nucl. Fusion 57, 056015 (2017)]. Central ion cyclotron resonance heating (ICRH) in the minority heating scheme has been compared with central and off-axis electron cyclotron resonance heating (ECRH), using both localized and broad heat deposition profiles. The transport coefficients have been calculated applying the gradient-flux relation to the evolution of the intrinsic W density in-between sawtooth cycles as measured using the soft X-ray diagnostic. For both ICRH and ECRH, the major player in reducing the central W density peaking is found to be the reduction of inward pinch and, in the case of ECRH, the rise of an outward convection. The impurity convection increases, from negative to positive, almost linearly with RF-power, while no appreciable changes are observed ...

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References
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Journal Article•DOI•
Neoclassical transport of impurities in tokamak plasmas

[...]

S.P. Hirshman1, D.J. Sigmar1•
Oak Ridge National Laboratory1
01 Sep 1981-Nuclear Fusion
TL;DR: In this paper, a closed set of moment equations is presented for the time evolution of thermodynamic and magnetic field quantities which results from collisional transport of the plasma and two-dimensional motion of the magnetic flux surface geometry.
Abstract: Tokamak plasmas are inherently comprised of multiple ion species. This is due to wall-bred impurities and, in future reactors, will result from fusion-born alpha particles. Relatively small densities nI, of highly charged non-hydrogenic impurities can strongly influence plasma transport properties whenever . The determination of the complete neoclassical Onsager matrix for a toroidally confined multispecies plasma, which provides the linear relation between the surface averaged radial fluxes and the thermodynamic forces (i.e. gradients of density and temperature, and the parallel electric field), is reviewed. A closed set of one-dimensional moment equations is presented for the time evolution of thermodynamic and magnetic field quantities which results from collisional transport of the plasma and two-dimensional motion of the magnetic flux surface geometry. The effects of neutral-beam injection on the equilibrium and transport properties of a toroidal plasma are consistently included.

1,081 citations

Journal Article•DOI•
The tokamak Monte Carlo fast ion module NUBEAM in the National Transport Code Collaboration library

[...]

Alexei Pankin1, D.C. McCune2, R. Andre2, Glenn Bateman1, Arnold H. Kritz1 •
Lehigh University1, Princeton Plasma Physics Laboratory2
01 Jun 2004-Computer Physics Communications
TL;DR: The NUBEAM module as mentioned in this paper is a comprehensive computational model for Neutral Beam Injection (NBI) in tokamaks, which is used to compute power deposition, driven current, momentum transfer, fueling, and other profiles.
Abstract: The NUBEAM module is a comprehensive computational model for Neutral Beam Injection (NBI) in tokamaks. It is used to compute power deposition, driven current, momentum transfer, fueling, and other profiles in tokamak plasmas due to NBI. NUBEAM computes the time-dependent deposition and slowing down of the fast ions produced by NBI, taking into consideration beam geometry and composition, ion-neutral interactions (atomic physics), anomalous diffusion of fast ions, the effects of large scale instabilities, the effect of magnetic ripple, and finite Larmor radius effects. The NUBEAM module can also treat fusion product ions that contribute to alpha heating and ash accumulation, whether or not NBI is present. These physical phenomena are important in simulations of present day tokamaks and projections to future devices such as ITER. The NUBEAM module was extracted from the TRANSP integrated modeling code, using standards of the National Transport Code Collaboration (NTCC), and was submitted to the NTCC module library (http://w3.pppl.gov/NTCC). This paper describes the physical processes computed in the NUBEAM module, together with a summary of the numerical techniques that are used. The structure of the NUBEAM module is described, including its dependence on other NTCC library modules. Finally, a description of the procedure for setting up input data for the NUBEAM module and making use of the output is outlined.

636 citations

Journal Article•DOI•
The nonlinear gyro-kinetic flux tube code GKW

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A. G. Peeters1, Yann Camenen1, F. J. Casson1, William Hornsby1, A. P. Snodin1, D. Strintzi2, Gabor Szepesi1 •
University of Warwick1, National Technical University of Athens2
01 Dec 2009-Computer Physics Communications
TL;DR: A new nonlinear gyro-kinetic flux tube code (GKW) for the simulation of micro instabilities and turbulence in magnetic confinement plasmas is presented in this paper, which incorporates all physics effects that can be expected from a state of the art gyro -kinetic simulation code in the local limit.
Abstract: A new nonlinear gyro-kinetic flux tube code (GKW) for the simulation of micro instabilities and turbulence in magnetic confinement plasmas is presented in this paper. The code incorporates all physics effects that can be expected from a state of the art gyro-kinetic simulation code in the local limit: kinetic electrons, electromagnetic effects. collisions. full general geometry with a coupling to a MHD equilibrium code, and E x B shearing. In addition the physics of plasma rotation has been implemented through a formulation of the gyro-kinetic equation in the co-moving system. The gyro-kinetic model is fivedimensional and requires a massive parallel approach. GKW has been parallelised using MPI and scales well up to 8192+ cores. The paper presents the set of equations solved, the numerical methods, the code structure, and the essential benchmarks. Program summary Program title: GKW Catalogue identifier: AEES_vI_0 Program summary URL: http://cpc.cs.qLib.ac.uk/summaries/AEES-vl-O.html Program obtainablefrom: CK Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL v3 No. of lines in distributed program, including test data, etc.: 29998 No. of bytes in distributed program, including test data, etc.: 206943 Distribution format. tar.gz Programming language: Fortran 95 Computer: Not computer specific Operating system: Any for which a Fortran 95 compiler is available Has the code been vectorised or parallelised?: Yes. The program can efficiently utilise 8192+ processors, depending on problem and available computer. 128 processors is reasonable for a typical nonlinear kinetic run on the latest x86-64 machines. RAM: similar to 128 MB-1 GB for a linear run; 25 GB for typical nonlinear kinetic run (30 million grid points) Classification: 19.8, 19.9, 19.11 External routines: None required, although the functionality of the program is somewhat limited without a MPI implementation (preferably MPI-2) and the FFTW3 library. Nature of problem: Five-dimensional gyro-kinetic Vlasov equation in general flux tube tokamak geometry with kinetic electrons, electro-magnetic effects and collisions Solution method: Pseudo-spectral and finite difference with explicit time integration Additional comments: The MHD equilibrium code CHEASE [1] is used for the general geometry calculations. This code has been developed in CRPP Lausanne and is not distributed together with GKW, but can be downloaded separately. The geometry module of GKW is based on the version 7.1 of CHEASE, which includes the output for Hamada coordinates. Runningtime: (On recent x86-64 hardware) -10 minutes for a short linear problem; 48 hours for typical nonlinear kinetic run. Reference: [1] H. Lutjens, A. Bondeson, O. Sauter, Comput. Phys. Comm. 97 (1996) 219, http://cpc.cs.qub.ac.uk/ surnrnaries/ADDH_v1_0.html Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

280 citations

Journal Article•DOI•
Kinetic calculation of neoclassical transport including self-consistent electron and impurity dynamics

[...]

Emily Belli, Jeff Candy
01 Sep 2008-Plasma Physics and Controlled Fusion
TL;DR: In this paper, the authors provide a first-principles based calculation of the neoclassical transport coefficients directly from solution of the distribution function by solving a hierarchy of equations derived by expanding the DKE in powers of ρ*i, the ratio of the ion gyroradius to system size.
Abstract: Numerical studies of neoclassical transport, beginning with the fundamental drift-kinetic equation (DKE), have been extended to include the self-consistent coupling of electrons and multiple ion species. The code, NEO, provides a first-principles based calculation of the neoclassical transport coefficients directly from solution of the distribution function by solving a hierarchy of equations derived by expanding the DKE in powers of ρ*i, the ratio of the ion gyroradius to system size. This includes the calculation of the first-order electrostatic potential via the Poisson equation, although this potential has exactly no effect on the steady-state transport. Systematic calculations of the second-order particle and energy fluxes and first-order plasma flows and bootstrap current and comparisons with existing theories are given for multi-species plasmas. The ambipolar relation ∑azaΓa = 0, which can only be maintained with complete cross-species collisional coupling, is confirmed, and finite mass-ratio corrections due to the collisional coupling are identified. The effects of plasma shaping are also explored, including a discussion of how analytic formulae obtained for circular plasmas (i.e. Chang–Hinton) should be applied to shaped cases. Finite-orbit-width effects are studied via solution of the higher-order DKEs and the implications of non-local transport on the validity of the δf formulation are discussed.

276 citations

Journal Article•DOI•
TORBEAM, a beam tracing code for electron-cyclotron waves in tokamak plasmas

[...]

Emanuele Poli1, A. G. Peeters1, G. V. Pereverzev1•
Max Planck Society1
01 May 2001-Computer Physics Communications
TL;DR: In this paper, the beam tracing technique is used to describe the propagation and absorption of Gaussian wave beams with frequencies in the electron-cyclotron frequency range in a fusion plasma.
Abstract: The beam tracing technique is used to describe the propagation and absorption of Gaussian wave beams with frequencies in the electron-cyclotron frequency range in a fusion plasma. Like in the standard ray tracing method, Maxwell's equations are reduced to a set of first-order ordinary differential equation. The technique employed here, however, allows for diffraction effects, neglected by the geometrical-optics procedure. The beam is specified in terms of the trajectory of the beam axis, the evolution of both the curvature of the wave front and the width of the field profile, as well as the absorption of the wave energy by the plasma. A Fortran code is presented, which solves the beam tracing equations in a tokamak geometry for arbitrary launching conditions and for both analytic and experimentally prescribed magnetic equilibria. Examples of wave propagation, power deposition and current profiles are computed and compared with ray tracing results.

222 citations

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Frequently Asked Questions (1)
Q1. What are the contributions in "A comparison of the impact of central ecrh and central icrh on the tungsten behaviour in asdex upgrade h-mode plasmas" ?

In this paper, a comparison of the impact of additional central ECRH and ion cyclotron resonance heating on the behavior of the tungsten ( W ) density in the core of H-mode plasmas heated with neutral beam injection ( NBI ) is performed in ASDEX Upgrade.