Nature of the Isotope Effect on Transport in Tokamaks M. Z. Tokar, D. Kalupin, and B. Unterberg Institut fu ¨r Plasmaphysik, Forschungszentrum Ju ¨lich GmbH, Association FZJ-Euratom, 52425, Ju ¨lich, Germany (Received 5 November 2003; published 28 May 2004) The reduction of energy and particle losses with the increasing mass of the hydrogen isotope is more pronounced under conditions of improved conﬁnement when the dominant ion temperature gradient instability is suppressed and other channels of anomalous transport are of importance. In this Letter, we reconsider the dissipative trapped electron (DTE) instability by taking into account ﬁnite Larmor radius effects in the analysis of the ion response to perturbations. By applying the improved mixing length approximation in order to estimate the transport coefﬁcients, it is demonstrated that DTE contribution is intrinsically dependent on the isotope mass and provides a plausible explanation for the isotope effect. Contrary to the common belief, it is shown that the DTE turbulence may be of importance for reactor plasmas of low collisionality. DOI: 10.1103/PhysRevLett.92.215001 PACS numbers: 52.35.Py, 52.55.Fa As observed in practically all tokamaks, the energy and particle conﬁnement improves with increasing atomic weight of the isotope used, from hydrogen to deuterium to tritium (see, e.g., Refs. [1–3]). This fact is of crucial importance for the performance of future thermonuclear reactors, which will operate with a mix- ture of deuterium and tritium rather than present devices which normally use either hydrogen or deuterium. However, in spite of its fundamental signiﬁcance, the isotope effect is still one of the least understood phenom- ena in the physics of tokamak transport. Analysis of the experimental database shows that the isotope effect on conﬁnement depends essentially on the mode of tokamak operation. Thus, the most recent scal- ings for the energy conﬁnement time  E [4] show in low (L) mode a rather moderate, as A 0:2 i , increase with the atomic weight A i . Plasma states, where improved conﬁne- ment is accompanied by peaked density proﬁles, reveal a signiﬁcantly stronger mass dependence. For example, in supershots in Tokamak Fusion Test Reactor (TFTR)  E scales as A 0:85 i [2], in pellet fueled plasmas in ASDEX [1], in the radiation improved (RI) mode in TEXTOR [5] and in discharges with improved Ohmic conﬁnement [1],  E  A 0:5 i . The latter dependence is also characteristic of the edge transport barrier in the H mode [3]. Conversely, in the core of H-mode plasmas the conﬁnement drops as A 0:2 i [3] and the overall H-mode isotope effect is similar to that in the L mode [4]. A pattern in this puzzling picture can be found by noting that the strongest improvement with A i takes place if the ion temperature gradient (ITG) instability, which is commonly considered as the main source of anomalous transport [6], is suppressed. This is the case both for the edge barrier in the H mode and for other regimes of improved conﬁnement where ITG is subdued by the den- sity gradient in a large part of the plasma volume (see, e.g., analysis of the L-RI transition in Refs. [7,8]). On the contrary, under conditions where the transport is domi- nated by ITG modes the conﬁnement deteriorates with increasing A i . For the case of the plasma core in the H mode, this fact was explained in Ref. [9] by applying the mixing length approximation (MLA) [6,10,11], in which  max =k 2 max is used as an estimate for transport coefﬁ- cients. Here  max is the maximum value of the instability growth rate  considered as a function of the perpen- dicular wave number k and k max is the k-value where  max is reached. For the ITG instability both  max and k max vary as A 0:5 i [6,12] and the characteristic heat diffu- sivity   A 0:5 i . Since  E  1=, the scaling above is in qualitative agreement with the decrease of the core con- ﬁnement in the H mode with increasing isotope atomic weight. The same result follows from the so-called im- proved mixing length approximation (IMLA) [6,13], which takes into account the phase shift between pertur- bations of the particle density and radial velocity. On this basis one can suggest that the positive isotope effect on conﬁnement is rooted in the inﬂuence of the ion mass on the transport channels that dominate when ITG turbulence is reduced or suppressed. In Refs. [14,15], in- stabilities driven by impurities were analyzed, and it was demonstrated that their growth rates are reduced with increasing A i . However, the importance of these instabili- ties for tokamak conﬁnement has been cast in doubt by the discovery of plasma states where anomalous transport is reduced due to the deliberate seeding of impurities [16]. A positive isotope effect was found also in numerical modeling of collisional drift turbulence [17]. However, this kind of turbulence is localized at the very plasma edge and cannot explain the modiﬁcation of proﬁles in the central region with varying isotope composition. In the plasma core, dissipative trapped electron (DTE) modes [11] are often considered as the most important under conditions where ITG activity is absent. The DTE instability is caused by the speciﬁc velocity dependence PHYSICAL REVIEW LETTERS week ending 28 MAY 2004 VOLUME 92, NUMBER 21 215001-1 0031-9007= 04=92(21)=215001(4)$22.50  2004 The American Physical Society 215001-1