Higher fusion power gain with profile control in DIII-D tokamak plasmas

. Strong shaping, favourable for stability and improved energy confinement, together with a significant expansion of the central region of improved confinement in negative central magnetic shear target plasmas, increased the maximum fusion power produced in DIII-D by a factor of 3. Using deuterium plasmas, the highest fusion power gain, the ratio of fusion power to input power, Q, was 0.0015, corresponding to an equivalent Q of 0.32 in a deuterium-tritium plasma, which is similar to values achieved in tokamaks of larger size and magnetic field. A simple transformation relating Q to the stability parameters is presented.

Canada. enhance plasma stability, experiments were carried out on DIII-D that significantly expand the fractional volume of plasma with improved core confinement to produce much higher fusion power gain, up t o QDD = 0.0015, in deuterium plasmas. This value of QDD corresponds t o an equivalent Q in a deuteriumtritium plasma, QDT = 0.32.
Normalized to the square of the toroidal field times the major radius, B t R 2 , the fusion gain results reported here are between 2 and 9 times larger than those achieved in other tokamaks. The product Bt R, proportional to the current through the centre post, is an important quantity in the tokamak as the dominant limitation of device construction is the stress limitation on this current. We will later show that BtR readily relates Q to the confinement and MHD stability properties' of the tokamak. These results offer the prospect of reduction in the size and field required for achieving higher gain, approaching fusion ignition conditions in a plasma, and support the viability of the concept [7] of a smaller, economically attractive tokamak reactor [8] through tailoring the equilibrium profiles.
It is well known that both fusion reactivity and plasma stability are sensitive to the form of the  pressure profile. Since an H mode plasma in DIII-D is characterized by a transport barrier at the plasma edge leading to a broader pressure profile, the presence of an edge barrier (H mode) or its absence (L mode) provides a degree of pressure profile control. Earlier experiments have shown improved core confinement with NCS plasmas in both L mode [9] and H mode [2] DIII-D plasmas. However, L mode NCS plasmas with strongly peaked pressure profiles were found to disrupt at PN values about a factor of 2 less than the values achieved in H mode [2, lo]. This lower beta limit in L mode is consistent with ideal MHD stability limits, and broadening the pressure profile is predicted to enhance stability and result in a large increase in plasma reactivity for strongly shaped plasma cross-sections [ll]. Experimental confirmation of these results, by demonstrating this increase in reactivity, was a strong motivating force for these experiments, where the L-H transition timing is used strategically to moderate the peaking of the pressure profile. This controlled transition has led to record reactivity for DIII-D plasmas, with QDD reaching values comparable to those in the larger, higher magnetic field tokamaks, J E T [12], JT-6OU [13] and TFTR [14].
The increase in achievable P and Q through a controlled L-H transition is shown in Fig. 1 where the evolutions of an L mode and of an H mode plasma are compared. Low power neutral beam injection (NBI) beginning at 0.3 s produces the NCS target [15]. Small, controlled changes in plasma shape induce an H mode transition in one case at 2.1 s, indicated by the edge pressure rise (Fig. l(c)). The L mode case disrupts at about 2.25 s ( Fig. l(a)). The H mode plasma continues to increase its stored energy and fusion reaction rate until a stability limit is reached at PN = 3.7. For this particular case, QDD reached 0.0012. The high performance phase is terminated by a global, P-limiting instability associated with the buildup of bootstrap-driven current density near the plasma edge [16], whereupon the plasma reverts to an ELMing H mode. The broadening of the pressure profile after the L-H transition is shown in Fig. 2, where profiles are shown just prior to the disruption of the L mode plasma and 0.125 s after the L-H transition for the H mode case.
The highest QDD discharge (87977, see Table I) was used as the basis for projecting the reactivity of a deuterium-tritium plasma under these conditions. The evolution of discharge 87977 is similar to that of discharge 87937, shown in Fig. 1. DT simulations based on discharge 87977, using the TRANSP [17] analysis code, predict QDT = 0.32, estimated as  Table I was measured with a calibrated scintillation counter.  ( ( p 2 ) / ( p ) ' ) , which increases with stronger peaking of the pressure profile. In Fig. 3 , we show good correlation of p r E with QDD in this experiment. Most of the scatter in Fig. 3 arises from the definitions of QDD with a denominator of input power (PNBI) and of 7 E with a denominator of loss power (PNBI -w), which differ under transient conditions.
We wish to express QDD in a way that incorporates the fundamental stability constraints of the tokamak, axisymmetric and kink stability. The strong shaping of DIII-D plasmas is a crucial factor in producing QDD values comparable to those of larger, higher magnetic field tokamaks. To illustrate this, we relate QDD to plasma geometry using an effective   [14] Ref. [13] Ref. [12] Ref. [  These parameters for determination of QDD are displayed in Table I1 for discharge 87977, compared with an earlier high performance VH mode plasma [20,211 in DIII-D as well as published data from other tokamaks. The dramatic improvements over earlier DIII-D results in fusion gain produced in these experiments derive in approximately equal measure from improved shape factor, lower q and improved confinement. For purposes of comparison with other published values we have plotted where Pt, Pbt and P b b are the fusion powers from thermal-thermal, beam-thermal and beam-beam reactions, respectively. Here, both the thermonuclear fusion reaction rate and the energy confinement time are referenced t o the input power that would be required t o sustain the plasma's thermal energy in steady state. As shown in Table 11, DIII-D has smaller Bt and R than the other tokamaks listed, but this is counterbalanced by the strong shaping and associated enhanced confinement [20] that allow it to operate at higher beta with modest input power. To more clearly demonstrate how these results extrapolate to requirements for achieving higher gain approaching fusion ignition conditions in a plasma, we separate the

p ( E 2 / E ) ( F 2 / q 2 ) .
Calculations similar to those in Ref. [8], with the reactor design systems code (Supercode), show that the capital cost of the tokamak reactor core increases approximately linearly with B:R2. As shown in Fig. 4, the ratio of fusion gain to this cost factor, Q&D/(B;R2), for the highest performance plasma in each device is adequately described by this simple expression. Details such as impurity concentration, individual For plasmas discussed here, the dominant power flow is through the ion channel which has confinement comparable to the neoclassical level [22] and an F value of 2.4. Thus, one does not anticipate much further enhancement of this quantity. The range of F in modern tokamaks is from about 1 to about 2. The remaining factors are bounded by ideal MHD stability. F is known [20] to exhibit strong dependence on E , q and the neutral pressure in the vessel. The relative importance of the individual terms in the abscissa is shown in Table 11.
Our present results represent a first attempt at control of the pressure profile in conjunction with current profile control. The L-H transition was used to provide stability through pressure broadening. Consistent with this, the observed limit in ,& is raised to about 4 from about 2 in the L mode. It is not known at present whether the H mode is playing a synergistic role as well in increasing the volume of plasma having reduced core transport. In Fig. 5, we show the pressure and safety factor profiles for discharge 87977, the highest QDD plasma. For comparison, we show the VH mode, which produced the highest neutron rate (discharge 78 136 in Table 11), and one of the best L mode plasmas. In comparison with the VH mode, we see that the region of low shear is expanded. The VH mode is calculated to be second stable [23] within p = 0.37, whereas discharge 87977 is second stable out to p = 0.7. This appears to be reflected in the pressure profile. The most dramatic difference is in the width of the ion temperature profile. The density profile is somewhat more peaked than for a VH mode, but remains very broad. While the L mode NCS plasma also has a large region with negative to neutral magnetic shear, as mentioned before, these plasmas with an L mode edge which show an internal transport barrier characteristically terminate in disruption at PN about 2.
Future experiments will attempt to regulate the heating power to avoid beta limits while exercising improved edge gradient control to maintain an attractive pressure profile and thereby extend these results to quasi-stationary operation. In a reactor embodiment of the tokamak, similar plasmas should be sustainable in steady state with modest radiofrequency driven current requirements [2]. These results are favourable for scaling to a compact fusion reactor [24].
In summary, fusion gain can be increased in four ways: increased size and field, B:R2, increased shaping, E 2 /~, improved confinement, F 2 , and increased peaking of the pressure profile, f,. By taking advantage of these improved stability properties that come from strang shaping and pressure profile control, combined with the improved confinement achieved in plasmas with negative central shear when high power neutral beam heating is applied, DIII-D has achieved high values of Q D D / ( B : R~) .