J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)469–472
000–000

Electron Cyclotron Radiation Studies
Using the ASTRA Transport Code Coupledwith the CYTRAN Routine
DIES Javier, GARCÍA Jerónimo, ALBAJAR Ferran, FONTDECABA Josep Maria,
CORTÉS Guillem and IZQUIERDO JesúsFusion Energy Engineering Laboratory (FEEL), Departament de Física i Enginyeria Nuclear,
ETSEIB, Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)(Received: 9 December 2003 / Accepted: 14 May 2004)

Abstract
The non-local effects of the EC radiative transfer on the electron temperature profile are analyzed for hightemperature plasmas as those expected in non-inductive ITER scenarios. For this purpose a 1D transport code has
been coupled with a model for the EC radiative power density, and the sensitivity of the electron temperature to thewall-reflectivity has been evaluated. The results obtained by letting the temperature as a free parameter show abroadening of the temperature radial profile when the non-local model is considered. Moreover, the temperature
resulting of the steady-state plasma equilibrium is shown to be strongly sensitive to the wall reflectivity.
Keywords:
Electron Clyclotron, advanced scenarios, ITER, energy transport

1. Introduction

2. Description of the plasma model

While Electron Cyclotron radiation losses are weak inpresent-day magnetically confined plasmas, these effects may
become important in next step devices, mainly due to theirstrong dependence on plasma electron temperature (Te),approximated by, Pcyc α Te5/2.
In 1D transport studies, the calculation of the Electron
Cyclotron (EC) power loss is generally performed using
locally applied global models [1,2]. However, it was shown[3,4] that a more accurate analysis is required owing to thenon-local nature of the radiation transport for the dominantpart of EC emission spectrum at the high temperatures
envisaged for plasmas of fusion interest [5]. These studies also
reveal that in the outer part of the plasma net EC power
absorption rather than emission may occur if the reflectivityof the wall is sufficiently high. Furthermore it is known thatfor ITER-like plasma conditions [6], at high electron
temperature as expected in the so-called “advanced” transportregimes, EC losses tend to be larger than bremsstrahlung
losses (although radiation as a whole remains much lessimportant as a transport channel than heat conduction).
In order to be able to take EC radiation effects
consistently into account, the ASTRA transport code [7] hasbeen coupled with the CYTRAN routine [4], which accounts
for essential parts of the non-local physics of the EC transport
process including wall reflection and which was shown toprovide a reasonable approximation to an exact treatment [3].

2.1 Thermal equilibrium and plasma
parameters
In order to reduce the effects involved in the electron
and ion thermal equilibrium of tokamak plasmas, the source
powers are grouped in a unique and fixed term Psource ,fPe Psource = Pe→i + PB + PEC + Pcon,efPi Psource + Pe→i = Pcon,i(1)where fPe,i is the fraction of source power coupled to theelectrons and ions ( fPi = 1 – fPe), PB is the bremsstrahlung
power loss, PEC is the EC power loss, Pcon is the conductiveconvective power loss, and Pe→i is the electron ion heatexchange due to Coulomb collisions. The electron density
being also fixed, the only variable in Eqs. (1) is thetemperature.
Throughout this study, the plasma is considered to havea circular plasma cross-section, in order to minimize
geometric influences over thermal transport, with major radius
R = 6.2 m, minor radius a = 2 m, and with the following
values for the magnetic field at the plasma axis, Bt = 5.3 T,
and plasma current, Ip = 15 MA. The electron density is taken
to be almost flat, ne = ne0(1 – ρ2)0.1, where ρ is the normalizedminor radius and ne0 = 7 × 1019 m–3. The total source power
follows a Gaussian radial profile with Psource = 100 MW. Thesevalues are based on non-inductive ITER scenarios [8] and©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: javier.dies@upc.es
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Dies J. et al., Electron Cyclotron Radiation Studies Using the ASTRA Transport Code Coupled with the CYTRAN Routine

scaled according to the lower plasma volume of the circularcase.

simple model is commonly used in some 1D transport studies.
In steady-state conditions and for a very optimistic wallreflection coefficient of Rw = 0.9 the resulting EC radiative
power density (dPEC /dV ) and electron temperature using one
or the other model for the dPEC /dV calculation are presented
in Fig. 1. Although both models give approximately the same
total EC power loss (PEC ~ 12.2 MW), when using the localmodel (Trubnikov’s formula) the dPEC /dV decay is slower andthe reversal of the net EC power density in the plasma outeris not reproduced. This qualitative difference enhanced forhigh wall reflectivities, being extreme for the ideal perfectwall case (Rw → 1), where the dPEC /dV curve using the local
formula is zero whilst the non-local model predicts an energy
redistribution from the plasma core to the outer plasma, theouter plasma being actually heated.
This energy redistribution due to the transfer of EC
radiation is confirmed when the corresponding electron
temperatures with Rw = 0.9 in steady-state conditions areanalyzed. While the electron temperature resulting of theequilibrium of ASTRA coupled with CYTRAN (the solid
curve of the right-side plot) presents three very well
distinguished regions,- a core region with a high and almost flat temperature
up to a normalized radius of about 0.3,
- an intermediate region with a strong Te gradient goingfrom high values (~ 37 keV) to low values (~ 6 keV),- and the slowly decaying edge region,
the electron temperature when using the local formula
presents a very small flat region at the plasma core (up toρ ~ 0.15), having a lower temperature at the intermediateradius 0.4 <∼ ρ <∼ 0.7. These results are in agreement with thoseobtained in [11] for D-D burning thermonuclear tokamak
plasmas.

2.2 Heat transport model
A very simple heat transport model giving electron
temperature profiles consistent with the observed advanced
regimes [9,10] is introduced in ASTRA code. The expression
for the electron and ion thermal diffusivities is:

χe,i = βe,i χi,neo + αe,i [H(ρ – ρ1) – H(ρ – ρ2)]
where the coefficients βe, βi, αe, αi, ρ1 and ρ2 are adjusted togive consistent electron temperatures profiles, and χi,neo is theneoclassical ion thermal diffusivity.

3. Effect of a non-local model for thecalculation of the EC radiative transfer
on the electron temperature profile
The CYTRAN routine, which is a non-local model forthe calculation of the EC radiative power density, is compared
to a local model, the Trubnikov’s formulad PTrubdV

locallyapplied (using the local values of temperature, density andmagnetic field for each unit of plasma considered),d PTrub(ρ)
dV= CT (1 – Rw ) a –1/2 Te (ρ) BT0 (ρ) ne (ρ)
1/2

5/2

5/2

1/2

1 + Φ (ε, Te )1/2

with CT ≅ 1.312 × 10–1 (when using SI units except for thetemperature, which is expressed in keV), and whereΦ ≅ 18ε , with ε = a/R, accounts for the inhomogeneity
1/2T e (ρ)

of the magnetic field due to toroidal geometry [1]. Such aρρFig. 1On the left-side plot, the EC radiative power density calculated using a non-local model (CYTRAN routine), the solid curve, or alocal formula, the dashed curve, and on the right-side plot, the corresponding electron temperature in thermal equilibrium.

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Dies J. et al., Electron Cyclotron Radiation Studies Using the ASTRA Transport Code Coupled with the CYTRAN Routine

3.1 Sensitivity of the thermal plasma
equilibrium to the wall-reflectivity

absorption when Rw increases is partially compensated by theobserved increase of the temperature, the competition between
both effects (self-absorption and emission) being favorable tothe first one. This trend is maintained for the entire plasma,and is especially dominant at the intermediate region, where
the self-absorption is higher.
Let us analyze in detail the dependence of the electron
temperature on Rw . Being the electron temperature a freevariable in our study and the total source power a fixed one,the electron temperature always increases with Rw in order toobtain a thermal equilibrium in steady-state conditions. In thecontrary case, all the terms of power losses, i.e. EC andbremsstrahlung radiative losses and the conductive-convective

Using ASTRA code coupled with CYTRAN routine, theeffect of the wall-reflectivity on the plasma equilibrium isshown in Fig. 2.
In this figure it is observed that when the wall-reflection
coefficient Rw increases, on the one hand, the EC radiative
power density decreases and the reversal of dPEC /dV at theintermediate region is enlarged, and, on the other hand, theelectron temperature increases.
This decrease of dPEC /dV was already obtained inprevious studies [3], where the temperature profile was fixed.
In the present case, the enhancement of the radiation self-ρρFig. 2EC power density and electron temperature in steady-state conditions for different values of the wall-reflection coefficient Rw.

Fig. 3On the left-side plot, electron and ion diffusivities as a function of the radial coordinate ρ, and, on the right-side plot, the radial
profiles of the source power density, EC and Bremsstrahlung radiative losses, and conductive-convective power loss, for awall-reflection coefficient of Rw = 1.

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Dies J. et al., Electron Cyclotron Radiation Studies Using the ASTRA Transport Code Coupled with the CYTRAN Routine

losses, would decrease while maintaining the total source
power term. In addition to this, for very high values of Rw ,the resulting profile reversal of dPEC /dV produces a steeper
temperature gradient at the intermediate region, making toincrease significantly the electron temperature at the plasmacore.
The terms of the thermal plasma power equilibrium insteady-state conditions are evaluated for the ideal limit case
Rw = 1, in order to emphasize the influence of the profile
reversal of dPEC /dV. As it can be shown in Fig. 3, the EC
radiative power density represents the dominant term of power
losses at the plasma core (for the range 0 < ρ <∼ 0.3), being
three times higher than bremsstrahlung losses at ρ = 0 (thisratio is still increased for lower values of Rw). The profile
reversal of dPEC /dV, localized in the range of 0.4 <∼ ρ <∼ 0.7,represents an important heating of up to 30% with respect tothe power source.

coefficient, this effect being strongly enhanced for high valuesof wall-reflectivity, where the reversal of the EC power
density at the intermediate region makes to increase thetemperature gradient, and consequently the temperature at theplasma centre.

References[1] B.A. Trubnikov, Reviews of Plasma Physics (M.A.
Leontovich, Ed.) Vol. 7, Consultants Bureau, New York,345 (1979).
[2] F. Albajar, J. Johner and G. Granata, Nucl. Fusion 41,665 (2001).
[3] F. Albajar, M. Bornatici and F. Engelmann, Nucl. Fusion
42, 670 (2002).
[4] S. Tamor, Rep. SAI-023-81-189-LJ/LAPS-72, Science
Applications, Inc., La Jolla, CA (1981).
[5] M. Bornatici, R. Cano, O. De Barbieri and F.
Engelmann, Nucl. Fusion 23, 1153 (1983).
[6] ITER-FEAT Outline Design Report, ITER EDA
Documentation Series No. 19, IAEA, Vienna (2001).
[7] G. Pereverzev et al., Report IPP 5/42 (1991).
[8] B.J. Green et al., Plasma Phys. Control. Fusion 45, 687(2003).
[9] JET Team, Nucl. Fusion 39, 1227 (1999).
[10] S. Ishida and the JT-60 Team, Nucl. Fusion 39, 1211
(1999).
[11] D.C. Baxter and N. Byrne, Nucl. Technology/Fusion
Vol. 3, 236 (1982).

4. Summary
The non-local effects of the EC radiative transfer on theplasma temperature profile have been evaluated for hightemperature plasmas, by using the ASTRA transport code
coupled to a model for the calculation of the EC radiativepower density. The energy redistribution produced by theplasma self-absorption of the EC radiation (non-local effect)
has a qualitative effect on the plasma temperature. When thetotal power source and density is fixed, the electron
temperature profile increases with the wall-reflection

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