1. HL-2A
TH/P2-19
Evolution of Ion Heat Diffusivity and Toroidal Momentum Diffusivity during Spontaneous ITB Development in HL-2A
EX/P8-10
TF Ripple Induced Stochastic Diffusion of Energetic Particles in Advanced Tokamak Configurations on HL-2A
Qingdi Gao1), R. V. Budny2)
1) Southwestern Institute of Physics (SWIP), Chengdu, China
2) Princeton Plasma Physics Laboratory, Princeton, USA
Introduction
Requirements to form ITB
Most theoretical models for the ITB formation ultimately rely on the suppression of micro-instability induced transport by sheared E×B flows, which is supported by experimental observations of these near ITBs. Different models emphasize different contributions to the E×B flow arising from the distinct terms in the radial ion force balance equation for the radial electric field,
i.e. the radial ion pressure gradient and the poloidal and toroidal flows, Vp and Vt, respectively (Bp and Bt are the corresponding magnetic fields).
Toroidal momentum torques generating Vt affect ITB evolution and decay in TFTR, JT-60U and DIII-D[1-3], which suggests that momentum inputs could offer a means for controlling barrier dynamics. An important question is whether it is possible to produce and control an ITB with inputting toroidal momentum in a discharge.
In order to explore the role of the external inputs of toroidal momentum on the development of ITBs we model the neutral beam heating discharges in HL-2A (R=1.64m, a=0.4m, Bt=2.8T, Ip=0.48MA) by using TRANSP.
The conditions for ITB formation, at a macroscopic level, are usually expressed in need of two things
1) Many experiments showed that negative or low magnetic shear is one of the essential gradients for the formation of ITB.
0.5MW LH wave is injected in the current drive mode (the multi-junction antenna phasing  = 90) to optimize q-profile.
Since the 2.45 GHz LH wave drives off-axis current in HL-2A[4], the q-profile with weak shear is established after the current profile sufficiently relaxed (at t~1.15s). It is sustained until LHCD is turned off (Fig. 1).
Fig. 1 q-profiles at different times after LHCD control. Dotted line is the q-profile before LHCD.
2) In addition to the presence of particular classes of q-profiles, a threshold power is requested to form ITB.
Experimentally, the formation of ITBs is sensitive to the power deposition profile and is influenced by the shape of the q profile and also affected by momentum inputs.
The parametric dependence, in terms of the global plasma parameters, of the ITB formation power threshold for the operation scenario here (i.e. in configurations with weak or negative magnetic shear and under dominant ion heating), has been obtained by regression analysis[5]:
3MW NBI power gives some margin to both the threshold power of ITB and that of H-mode.
The modeled discharge: Bt = 2.6T, Ip = 300kA, , single null divertor, and H-mode boundary.
To achieve ITB, 3MW NBI heating (E=45keV) during t= s.
To control the current profile, 0.5MW LH wave injection during t= s
Spontaneous development of ITB
The heat and momentum transport is calculated with GLF23 when r < 0.9, and 5×neoclassical when r > 0.9. The GLF23 model is a physics-based model that was developed from 3D gyrokinetic stability calculations for the linear growth rates and from 3D nonlinear gyro-Landau-fluid simulations used to determine the saturation levels[6].
The neutral beam is injected tangentially with both co- and counter-injection to control the momentum input.
With appropriate neutral beam injection, the nonlinear interplay between the transport determined gradient lengths in Vt and Ti,e and the E×B flow shear (including q-profile) produces transport bifurcations, leading to a stepwise growing ITB (Fig. 2a). After its growth duration steady ITB with H-mode edge is formed at t~1.35s and sustained until the NBI heating is turned off.
Plasma performance upgrades in the ITB phase
In the best ITB configuration (as shown in Fig. 2) the confinement enhancement factor over ELMy H-mode scaling, H98(y,2), increases significantly, from around 1.1 before the ITB developed raising to more than 1.5 in the whole ITB phase (Fig. 3a).
The ITB phase is also characterized by a quite large increment of the normalized β and fraction of bootstrap current (Fig. 3b,c).
Fig. 3 Plasma performance parameters versus t: (a) confinement enhancement factor, (b) normalized β, (c) fraction of the bootstrap current.
Exhibitions of the barrier formation in the particular transport channels vary. As usually observed in the NBI heating discharges, barriers form most readily in Ti, Vt, but barrier in Te more resistant to form (Fig. 2b).
Fig. 2 (a) Evolution of Ti-profile, showing the ITB development generated by using the NBI of 2.5MW (co) + 0.5MW (ctr), (b) profiles of Ti, Te, and toroidal angular velocity wt in the ITB phase at t=1.5s
ITB development is dependent on the NBI injection
Low confinement enhancement in ITB with L-mode edge
Quasi-steady ITBs can not be established unless the co-injected NBI power is in the range of 2.85MW to 2.4MW (correspondingly the counter-injected power is 0.15MW to 0.6MW respectively).
If all the 3MW NBI power is co-injected a quasi-steady ITB configuration can only be formed with L-mode edge in Te (Fig. 4).
Fig. 5 Comparison of Te-profiles between (a) ITB configuration produced by 3MW NBI all co-injected and (b) that produced by NBI of 2.5MW(co) + 0.5MW(ctr).
In the plasma produced with the 3MW NBI power all co-injected, there no pedestal exists in Te-profile during the ITB phase (Fig. 5a), and the tempera-tures achieved are much lower than that in the discharge shown in Fig. 2.
Since neither obvious internal barrier nor edge barrier is developed in Te, the integrated Te is even lower than that before the ITB developed. Thus improve-ment of the global energy confinement in the ITB phase is unobvious.
Fig. 4 (a) Evolution of Ti-profile, showing the ITB with L-mode edge generated as the 3.0MW NBI power all co-injected, (b) profiles of Ti, Te, and wt in the ITB phase at t=1.5s
Qingdi Gao et al th IAEA Fusion Energy Conference, October 2012, San Diego, USA TH/P2-19

2. Evolution of thermal conductivity and viscosity
E×B flow shear suppresses turbulent fluctuations
The ITB formation process is quite dramatic with abrupt transitions in the temperatures and toroidal rotation as their profiles evolve. The transitions are transport related and mainly a result of competition between the toroidal flow and diamagnetic terms within the E×B shear rate. Thus it is worthwhile to study the relationship between viscosity and ion heat transport in the ITB formation process.
The temporal evolution of toroidal momentum diffusivity cm and ion heat diffusivity ci in a region around the ITB development were examined.
As shown in the following figure (Fig. 6), the transport barrier of momentum develops more quickly and its enhanced confinement region extends further outward than that of heat.
The E×B flow shear can lead to a reduction in the amplitude of turbulent fluctuations, even to their suppression, or to a decrease in the radial correlation lengths, i.e. a breaking up of turbulent eddies, both effects producing a decrease in turbulent transport.
The E×B flow shear is characterized by the shearing frequency, wE, the radial shear in the E×B velocity, and a criterion for the suppression of micro-instabilities, based on the numerical simulations of ITG turbulence, has been proposed:
where gLin is the linear growth rate of a drift wave instability in the absence of the sheared rotation, and wE is defined as[6]
It is encouraging that experimental values of wE at ITB formation are consistent with criterion (3).
gLin is predicted by GLF23 model, and wE computed self-consistently according to equation (1) and (4).
Before the ITB developing (e. g. at t=1.22s), both cm and ci are much higher than neoclassical level, while there exist abrupt diffusivity drops at some points. The ITB develops with the drops growing down. cm is reduced to the neoclassical level at r = 0.7 at t=1.23s. Then the region of neo-classical level expands around r = 0.7: extending inward to the whole central plasma region first at t=1.291s; then outward to r =0.8 at t=1.3s (Fig. 6a-f), result-ing in steady momentum transport barrier until NBI turns off.
The reduction of ci is slower than that of cm while the ITB developed. The drops in ci grows down mildly and it is reduced to the neoclassical level at r =0.55 at t=1.285s. Afterword, the region of neoclassical value expands: first extending outward to r = 0.6 at t=1.291s, and then inward to the most central region at t=1.348s, forming a steady heat transport barrier (Fig. 6b-f).
Fig. 7 Spatio-temporal contours of (a) linear growth rate of leading mode of the drift ballooning instability gLin, and (b) E×B shearing frequency wE.
gLin is rather low (gLin≤0.1s-1) before t~1.25s except in the edge plasma region (r >0.8). Then it grows up with the plasma parameters increasing, forming two peaks: one at r ~ 0.6 with the peak value around 0.4s-1, and another at r≤ 0.8 with the peak value around 0.5 – 0.6s-1 (Fig. 7a).
before t ~ 1.25s wE is less than gLin (even though gLin is rather low). With the ITB developed both dpi/dr and Vt increase, raising the sheared E×B flow. This positive feedback produces a quite broad region of wE>0.6s-1 (shaded area in Fig. 7b) which covers and exceeds the two maximums of gLin after t=1.3s. The criterion for the suppression of microinstabilities is satisfied, and quasi-steady ITB can be formed.
Fig. 6 cm (red line) and ci (blue line) versus r while the ITB developed for the discharge shown in Fig. 2. Black dotted line is their neo- classical value.
Influence of Vt on driving transport bifurcation
NBI driven toroidal flow drives transport bifurcation
Many theoretical models were developed to explore features of the transport bifurcation dynamics. In the models based on the transport bifurcations arising from E×B suppression of turbulent the diffusion coefficients often use the forms:
Such an approach (with n = 2) was pioneered by Hinton and Staebler[7] using a drift wave transport model, and core ITB bifurcations were found. A study of the form (5) has also been performed by Horton and Zhu[8]. Taking the dTi/dr contri-bution to wE they found that a strong bifurcation could only be achieved with n ≥ 4, provided the dimensionless power,
exceeds a critical threshold value, Pc (~10). For n = 4 they found Pc≈7.
Here, we take rdp the radius of ITB foot, and n0 and T0 the pre-ITB values, then Pc≈5, which means that the transport bifurcation can be achieved here with lower Pc. One of the reasons causing Pc lower may be due to the contribution arising from the NBI driven Vt to the E×B shearing flow.
To understand the key roles played by the NBI driven toroidal flow in triggering the transport bifurcation, we compare the different contributions to the E×B flow arising from the distinct terms in Er (equation (1)), namely Vt term (contribution from the NBI driven toroidal flow), dpi/dr term (contribu-tion from the ion pressure gradient), and Vp term (contribution from the poloidal plasma flow).
In the E×B flow the Vt term and the dpi/dr term can be determined by transport equations with heating and momentum inputs, the Vp term is taken from neo-classical theory, using the NCLASS code.
Conclusions
Fig. 8 Contributions to the E×B flow from (a) Vt, (b) dpi/dr, and (c) Vp while the ITB developed at t=1.3s (red line) and t=1.35s (black line).
Spontaneous development of ITB in HL-2A is modeled.
The NBI heating dischages is simulated with physics-based transport model GLF23.
With appropriate neutral beam injection, complicated interplay between the transport determined gradients in Vt and Ti,e and the E×B flow shear (including q-profile) produces transport bifurcations, developing spontaneously ITB.
The ITB establishment is dependent on the toroidal momentum input. Quasi-steady ITBs with H-mode edge can not be established unless the co-injected NBI power is in the range of 2.85MW to 2.4MW out of the total 3MW. Quasi-steady ITB configuration can only be formed with L-mode edge in Te if the 3MW NBI power is all co-injected.
Temporal evolution of the ion conductivity and viscosity is examined.
The transport barrier of momentum develops more quickly and its enhanced confinement region extends further outward than that of heat.
The earlier improvement of the momentum confinement causes the E×B flow to increase significantly, which would trigger the ITB development.
Suppression of turbulence by shearing E×B flow is evaluated.
As the enhanced momentum confinement extended further outward, a broad region of high E×B shearing frequency is produced, which covers and exceeds the separated peaks of the instability growth rate, satisfying the criterion to suppress turbulence.
By comparing the different contributions to the E×B flow arising from the distinct terms in the radial ion force balance equation of Er, it is found that the broad region of high E×B shearing frequency can not be achieved without the contribution from Vt.
The Vp term (Fig. 8c) is about two order smaller than the Vt term, ignorable.
The raise of dpi/dr term (Fig.8b) comes mainly from the build-up of higher Ti gradient while the ITB developed. It is very localized around r ~ 0.6 (in the Ti barrier region) and can not play roles in raising wE at r ~ 0.8 where the second peak of gLin is located. Therefore, with the dpi/dr term only it is impossible to produce the broad region of high wE like that shown in Fig. 7b.
In view of the region covered by the high Vt term is rather wide (Fig. 8a), it can produce the broad region of high wE, leading to stable ITB.
According to analysis on the evolution of diffusivities, the toroidal momen-tum diffusivity is reduced to the neoclassical value before the Ti barrier formed. The earlier improvement of momentum confinement causes E×B flow to increase significantly, which is possible to trigger the ITB development.
References
Levinton, F. M., et al., Proc. 16th Int. Conf. on Fusion Energy (Montreal, 1996) vol 1 (Vienna: IAEA) p 211 (1997)
Shirai, H., et al., Nucl. Fusion 39 (1999) 1713
Doyle, E.J., et al., Nucl. Fusion 42 (2002) 333
Gao, Q. D., et al., Nucl. Fusion 47 (2007) 1318
Sips, A. C. C., et al., Plasma Phys. Control. Fusion 44 (2002) A391
Waltz, R. E., et al., Phys. Plasma 4 (1997) 2482
Hinton, F. L. and Staebler, G. M., Phys. Fluids B 5 (1993) 1281
Horton, W. and Zhu, P., Phys. Plasmas 7 (2000) 4534
Qingdi Gao et al th IAEA Fusion Energy Conference, October 2012, San Diego, USA TH/P2-19