This erratum reports on an incorrect result presented in Ref. 1 dealing with gyrokinetic simulations including the centrifugal force in a rotating plasma. The formulation of the model used in Ref. 1 is based on the equations derived in Ref. 2, and it has recently been pointed out3 that the model is missing a term in the radial derivative of the Maxwell distribution, connected with the free energy in the rotation profile. For the case of a strongly rotating plasma with a local rotation gradient, the equations of Ref. 1 should be modified: The Ω appearing in Eqs. (5)–(7) of Ref. 1 should be interpreted as the plasma rotation frequency ωϕ, which can have a radial variation (unlike the rotation frequency Ω of the rigidly rotating frame). Since the gyrokinetic equation is formulated in the local limit with the rotation frequency of the rigidly rotating frame (Ω) equal to the plasma rotation (ωϕ) at the local surface considered, this difference is important only when radial derivatives are taken. Equation (12) of Ref. 1 then becomes

RLnERLn|R0=(Teψ+Tiψ)miΩ2(R2R02)2(Te+Ti)2miΩ2Te+Ti(RRψ|θR0R0ψ|θ)+ωϕψΩmiT(R2R02)
(12)

and Eq. (14) of Ref. 1 becomes

S=vE·[nR0nR0mΩ2TR0R0ψ|θψ+(v2vth2+(μB+E)T32)TT+(mvRBtBT+mΩT[R2R02])ωϕ]FMZeTdXdt·ϕFM.
(14)

The additional terms given above have recently been implemented in the gyro-kinetic flux tube code GKW.4,5

Almost all results presented in Ref. 1 deal with a strongly rotating plasma with no local rotation gradient (ωϕ=0) and, consequently, are not affected by the new terms given above. Only the result in Sec. IV B for the Cu coefficient (Fig. 10) needs to be revisited. This figure is reproduced here including the new terms. It can be seen that the new term has a significant impact on the results; the coefficient Cu changes sign for the ITG case, and is much larger for the TEM case considered. The result shown in the figure represents the case in which the bulk plasma species have no rotation gradient, but the impurity species is given an independent rotation gradient for calculation of Cu. The convective pinch coefficient Cp is unchanged for this (somewhat unphysical) case. In general, however, the rotation gradient of the bulk plasma species enters in radial derivative of the centrifugal potential Φ and can have a significant influence on Cp (see Refs. 6 and 7). The impurity transport results presented in Ref. 1 therefore describe one specific case and should not be considered to be generic results for ITG or TEM.

FIG. 10.

(Updated) Rotodiffusive coefficient Cu for trace species deuterium, helium, carbon, and tungsten for GKW-ITG and GKW-TEM cases both with kθρs=0.304.

FIG. 10.

(Updated) Rotodiffusive coefficient Cu for trace species deuterium, helium, carbon, and tungsten for GKW-ITG and GKW-TEM cases both with kθρs=0.304.

Close modal

The influence of the new terms is significant only for particle and impurity transport. However, it can be seen from the modified Fig. 10 that the difference in impurity transport due to these new terms can be substantial. In general, therefore, the additional radial gradient in the background distribution cannot be neglected for a strongly rotating plasma with a nonuniform angular rotation frequency.

The authors are grateful to C. Veth for his careful work in following a discrepancy in the 2D reconstruction of the density distribution, which led him to discover the oversight described above.

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The latest version of the GKW code is available from http://gkw.googlecode.com.
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