PHYSICS OF PLASMAS
VOLUME 9, NUMBER 12
DECEMBER 2002
ERRATA
Erratum: ‘‘Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime’’ †Phys. Plasmas 6, 2834 „1999…‡ O. Sautera) and C. Angioni Centre de Recherches en Physique des Plasmas, Association EURATOM-Confe´de´ration Suisse, Ecole Polytechnique Fe´de´rale de Lausanne, 1015 Lausanne, Switzerland
Y. R. Lin-Liub) General Atomics, San Diego, California 92186-5608
共Received 3 September 2002; accepted 3 September 2002兲 关DOI: 10.1063/1.1517052兴
Note that the term was correctly included in the last equation on p. 2839, but the typical values for the different terms are L31⬇L34⬇⫹0.5, L32⬇⫺0.2, ␣⬇⫺0.5, and R pe ⬇0.5. Another useful way to define the bootstrap current with only a few parameters, for magnetohydrodynamic studies, for example, is to use R pe ⫽ p e /p and ⫽ ln T/ ln n and to assume similar scalelengths for the different species. In this way the last equation on p. 2839 simplifies to
The authors apologize for this late correction of a few errors which appeared in our paper. The main one is the sign of the coefficient 0.315 in Eq. 共17b兲 on p. 2838, which should be positive, and therefore replaced by
␣共 i 兲⫽ *
冋
␣ 0 ⫹0.25共 1⫺ f 2t 兲 冑 i 1⫹0.5冑 i
⫻
1 1⫹0.15 i2 f 6t
*
* ⫹0.315 2 f 6 i * t
册
.
*
具 j 储 B 典 ⫽ neo具 E 储 B 典 ⫺I 共 兲
This was defined such as to obtain the correct limit at large collisionality, 0.315/0.15⫽2.1, as shown in Fig. 7 on p. 2838. Also in these formulas Z usually refers to the effective charge Z eff , except for the ion terms Eqs. 共18c兲 and 共18e兲, where it should be replaced by the main ion charge Z i . In the last but one equation, a term is missing, as seen from the definition of A 4 in Eq. 共6兲 on p. 2835, and it should read
具 j 储 B 典 ⫽ neo具 E 储 B 典 ⫺I 共 兲 p e
冋
⫻ L31
⫻
L31
册
⫹R pe 共 L31⫹L32兲 ⫹ 共 1⫺R pe 兲共 1⫹ ␣ 兲 L31 ,
where the fact that L 34⬇L 31 has been used and the terms in the square brackets have been grouped such as to give the relative contributions due to the density, electron temperature and ion temperature gradients, respectively. This gives a simple dependence of the bootstrap current on the plasma profiles. Using the typical parameters mentioned above, in the limit of flat density profiles like in high confinement modes 共H modes兲 共→⬁兲, one gets a coefficient of 0.28, whereas for similar temperature and density scalelengths 共⫽1兲 one gets 0.39, that is about 50% more bootstrap current due to the contribution from the density gradients.
册
p ln p ln T e 1⫺R pe ln T i ⫹L32 ⫹L34 ␣ . pe R pe
a兲
Author to whom correspondence should be addressed. Electronic mail:
[email protected] b兲 Present address: Department of Physics, National Dong Hwa University, Hualien, Taiwan, ROC.
1070-664X/2002/9(12)/5140/1/$19.00
冋
p ⫹1
5140
© 2002 American Institute of Physics
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