Requirements for advanced tokamak (AT)

A steady state advanced tokamak must achieve both high beta and high confinement, consistent with a high fraction of the plasma current being carried by the boothtrap effect.

High confinement, to permit high Q at reduced machine size and/or magnetic field.

The ignition margin

Mig ( P(/Ploss ( /(/(E)=(E/2

Taknig a convenient generic confinement scaling,

(E ( HIpR1.5k0.5Ptot-0.5 (J. G. Cordey, R. J. Goldston, R. R. Parker 1992)

(E ( H2Ip2A2, /2 = ((*/()2

Mig ( Ip2A2H2((*/()2 = Ip2A2H*2 (H* ( H(*/()

High beta, to achieve high power density for given magnetic field at the toroidal field coil.

(B02 ~ Bcoil = constant (for ( = 1/3 ~ 1/5)

1/2 ~ (*B02 ( A(* = 5(N*/qcyl ( (N* = (*/(Ip/aB0)

High usable bootstrap fraction, to gain high non-inductive driven current.

The bootstrap fraction

Ibs/Ip ( 0.6 (1/2(p

(p = 0.05(Nq*/(, q* (

Ibs/Ip ( A1/2(Nkqcyl

These must be achieved consistently with:

High plasma density (rather somewhat exceeding the Greenwald density)

Highly dispersive divertor operation

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1. Plasma shaping Elongation is beneficial to plasma confinement by increasing the current holding capacity .

Triangularity is beneficial to supresion some MHD instabilities

Quadrangle shaping showing evidence to modify ELMs (DIII-D)

Identification of the plasma boundaryEFIT code developed in GA has been used widely in the would for the plasma shaping control

Reconstructed boundary at 320ms for 2898 shot. (+ and + denotes the filament and the centroid of plasma current respectively. X point position (Xr=1.552m, Xz=-0.451m), the position of strike point Zi=-0.780m (inner), Zo=-0.812m (outer), the plasma geometric center (Rg=1.652m, Zg=-0.069m), the plasma current centroid (Rc=1.664m, Zc=0.007m), plasma minor radius ap= 0.380m, elongation k=1.085) Determination of the plasma boundary for the single null divertor plasma in HL-2A

Plasma shaping in HL-2A

The X-point is nearly fixed. To keep the plasma current holding capability the same as the circular plasmas, we have two options for the plasma shaping:

(a) shifting the X-point inward relative to the position of the plasma column;

(b) reducing the plasma radius on the mid-plane, while keeping significant triangularity.

Fig.2.1 Magnetic geometry of (a) a plasma with a nearly circular cross section, (b) a plasma with the X point moving inward (D-shape, k95=1.08, 95=0.44), (c) a plasma with modest elongation (elongated D-shape, k95 = 1.21, 95 = 0.41).

The triangularity variation with respect to the flux coordinate is dependent on the plasma current profile, but for both hollow and peaked current profiles it decreases rapidly at the plasma boundary region while moving towards the plasma center Fig.2.2 Triangularity of the D-shaped plasma, versus the flux surface for the cases of hollow current profile (full line) and peaked current profile (dotted line).

Control and optimization of the plasma current profile is a key point in enhancing the plasma performance. Although several tools have been identified to modify transport directly, the effect of the current profile on transport is large and remains an important transport control feature. HL-2A has two different RF systems. The LH power is generated with 2 klystrons 0f 0.5MW each and radiated by a multi-junction (212) antenna. The EC power is generated by 4 gyrotrons with 0.5MW each. Directions of the radiated EC beams can be varied toroidally and poloidally by rotating the steerable mirrors.

A tangential neutral beam line will be installed this year, with power of PNB = 2.0MW, and beam energy Eb = 50keV, and It will be upgraded to PNB = 3.0 MW. Another beam line is expected.2. Optimization of the plasma current profile

1. Quasi-stationary RS operation established with current profile control

To sustain RS operation towards steady state, the current density profile is controlled with LHCD (fLH = 2.45GHz)

RS discharges are modeled by using TRANSP code.

Brambillas coupling + LHCD package + TRANSP to get driven current in a dynamic case

Dispersion relation in the LH frequency domainFrequency domain wci

Wave propagation equations in the optical geometry:

Rays are radially reflected at the caustics,defined by:

propagation domains:

n||0: injected value; q = rBtor/RBpolRay tracing for LH waves

3 Fokker-Planck analysis Kinetic equation

An electron kinetic equation can be written as The wave diffusion operator is the 1-D divergence of the RF induced flux: where Dql is the quasi-linear diffusion coefficient, and here it signifies a sum over all waves in existence on a flux surface, with the appropriate powers and velocities. A simple sum is used, which means that we assume there are no interference effects.

We employ a 1-D collision operator as given by Valeo and Eder,with the collisional diffusion and drag coefficient given by In solving for fe we set , because the time for equilibration between RF power and the electron distribution is short compared with the time for plasma to evolve. Then the solution for fe is an integral in velocity space,

Control of the electron velocity distribution functionLH waves can drive a fast electron tailMaxwellian bulksuperthermal tail

a parallel velocity Fokker-Planck calculation for the interaction of wave and particles

,

,

,

.

Brambillas coupling + LHCD package + TRANSP to get driven current in a dynamic case

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Sustained RS operation mode

The target plasma is maintained by means of 2.0MW neutral beam (1.5MW co-injection and 0.5MW ctr-injection) injected into an ohmic heating discharge with modest peaking density profile (ne(0)/

=1.86,

). 0.5MW LH wave power at 2.45GHz ( = 90

) is used for profile control.

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Fig.1.1 Waveforms of the plasma current Ip, loop voltage Vp, the NBI power PNB, and the LH wave power PLH Fig.1.2 Magnetic geometry of the discharge

Fig.1.3 (a) The temporal evolution of LH wave driven current profile, and (b) q profiles at different times for the sustained RS discharge

A steady-state RS discharge is formed and sustained with

and

(

=3.0 - 3.2) until the LH power is turned off.

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Fig.1.4 (a) Waveforms of the plasma currents Ip, ILH, IBS, INB, and IOH and (b) their profiles at t=1.0s for the sustained RS discharge

----The RS discharge has achieved nearly a fully non-inductive current drive with non-inductive current fraction Fnon-inductive=90%

Fig.1.5 The ion temperature Ti (full line), and magnetic shear s (dotted line) versus x

Internal transport barrier

ITB appearing on the ion temperature Ti is kept stationary in the RS phase with the maximum of (Ti being near rmin .

In the sustained RS discharge an enhanced confinement with H98(y,2) (1.1 is obtained

During the RS discharge the temporal evolution of the location of ITB follows the evolution of the shear reversal point

Fig.1.6 Time traces of a quasi-stationary RS discharge: (a) LHCD efficiency, CD and non-inductive current fraction, (b) the H-factor, H98(y,2) and normalized beta, N, (c) the locations of the minimum q (full line) and the minimum i (dotted line), (d) the central plasma temperatures (Ti, Te).

The H-mode transport barrier is localized at the plasma edge;

The pressure of the H-mode pedestal increases strongly with triangularity due to the increase in the margin by which the edge pressure gradient exceeds the ideal ballooning mode limit;

Therefore, the rather high triangularity located at the plasma edge is favorable to enhancing the confinement.

RS discharge with double transport barrier

The elongated D-shape plasma (98=0.43, k98=1.23) is used to model the RS discharge. The geometry of the boundary (98% flux surface of the diverted plasma) is specified as a general function of time. It evolves from circular to elongated D-shape during the current ramping-up phase and then keeping the same shaped boundary in the current flattop phase. The interior flux surfaces, which are computed by solving the Grad-Shafranov equation, are parameterized by the square root of the normalized toroidal flux.

The standard target plasma described above is used, but the electron density profile has a modest change with a more obvious edge pedestal.

The current profile is still controlled by LHCD.

The double transport barrier is indicated by two abrupt decreases of the ion heat diffusivity, of which the two minima are located near the shear reversal point, min 0.55, and near the plasma edge, 0.95, respectively. The elevated heat diffusivity between the two minima separates the two barriers. Fig.2.3 Profiles of q and ion heat diffusivity, i (at t=1.0s) for the elongated D-shape plasma. Fig.2.4 Profile of ion temperature and the ion temperature gradient, Ti (at t=1.0s).

Fig.2.5 Time traces of an RS discharge with double transport barrier: (a) normalized beta, N, (b) H-factor, H98(y,2), (c) locations of the double transport barrier (two dotted lines), and location of the shear reversal point (full line). The fainter lines indicate the results of the RS with L-mode edge.In the DB discharge the plasma confinement is enhanced, and normalized beta, N and H-factor, H98(y,2) are higher than in the RS configuration with L-mode edge (see Fig. 1.6)

Profile control by ECH+LHCDEmploying LHCD for large-scale q(r) control in a low-density plasma ofne =1.01019m-3 and Ip = 400kA, BT = 2.43T is considered. The target plasma is heated by EC of 0.48MW + 0.47MW lunched from 2 gyrotrons. By adjusting the polar lunch angle the EC power from 2 gyrotrons deposits around r = 0.2 and r = 0.3 respectively. The q-profile has a little change in the ECH phase. To control the current profile, 0.5 MW LH power in the current drive mode (the multi-junction antenna phasing =90) is injected. As the LH wave deposition primarily governed by a nonlinearity between the LH power deposition profile and the electron temperature profile, the q-profile adjusts slowly, and the safety factor between r=0.0 and r=0.7 evolves gradually to the new quasi-steady values on the resistive time scale.FIG. 8 Temporary evolution of q at various flux surfaces.

FIG. 9 (a) q-profiles, and (b) absolute value of magnetic shear versus r at various times, (c) Te-profiles at t=0.4s (Ohmic phase ),and t=1.3s, thin black line indicating electron heating power. After the current profile is fully relaxed, the q values of r = 0.0-0.6 constrict to a narrow range of 1.0-1.3 (Fig. 6), and a q-profile with weak shear region extended to x=0.6 and qa=3.21 is established. It is sustained until LHCD is turned off. Though the q-profile in the weak shear region is not as flat as that in the discharge controlled by ECCD, the absolute value of the magnetic shear s[(dq/dr)(r/q)] is rather low.The Te-profile does not show a change corresponding to the optimized current profile as is often the case with an electron-ITB developed.But the electron temperature increases largely, and its normalized gradient R/LT (where 1/LT = Te/Te) becomes larger than the critical gradient value (R/LT

Current profile at t = 1.4s: total plasma current jp (full line), ohmic current joh (thin full line), LH driven current jlh (dotted line), and EC driven current jecr (dashed line). Fully non-inductive current drive

NBIAT

For comparison, the above Ohmic plasma (Te>Ti) is heated by the same LH wave scheme only to establish hot electron scenario.

Higher power electron Landau heating establishes operation scenario of preferentially dominant electron heating. Electron tempera-ture increases significantly. In contrast to the large increment of the electron temperature, the ion temperature only has a small change (dotted lines in Fig. 4).In the hot ion plasma, not only the electron temperature has a large increment, but the ion temperature increases signifi-cantly (from Ti0 = 1.5keV to Ti0 ~ 2.6keV) as well (full lines).Fig. 4 Temporal evolution of Ti0 (blue line), and Te0 (purple lines). Full lines indicate hot ion mode (NBI+LH heating), and dotted lines indicate hot electron mode (LH heating only)

A comparison for the ion confinement is made between the RS and non-RS discharge: RS discharge - the LH wave is injected with slightly asymmetric spectrum ( = 170); non-RS discharge - the LH wave is injected with purely symmetric spectrum ( = 180), in this case the q-profile with negative shear could not be formed since the off-axis current driven by the LH wave is not sufficient.

The energy variation of the injected particles can be described with fairly accuracy by the following energy loss equation when With W in eV, the rate of the beam energy loss is If we consider beam particles of energy W which undergo complete therma-lization, then the average fraction of the total energy given up by the beam particles, which goes into the thermal ions of the plasma, is = To know the effect of LHH on the NBI power that goes into ions, it is essential to analyze how the ions and electrons are heated by the injected neutral beam.

Fig. 2 Average fraction of beam energy that goes into the thermal ions, F_ion, versus time, full line: Pbi/(Pbi+Pbe); dotted line: FiAs the electron temperature increasing due to LHH, the verage fraction of beam energy that goes into the thermal ions increases.However, when the many physics effects in the NBI heating is taken into account, the picture is different: the NBI power that goes directly into the bulk ions and the power introduced by thermalization of the beam ions compose the ion heating power, and it is nearly unchanged.

Fig. 3 (a) NBI heating power, and (b) NBI power losses versus time. Pbi is the NBI power that goes into ions, Pbe the NBI power that goes into electrons, Pbth the power from thermalization of the beam ions, Pcx the NBI power lost by charge-exchange, Pshin the NBI power shone through, Porb the orbit loss power of the beam ions, and Pie the power loss by electron-ion coupling inside the ion-ITB.

Plasma equilibrium in a tokamak with current hole Experimental results in JET Experimental results in JT-60U

M. S. Chus work

Revisited the theory of Greene,Johnson, and Weimer [Phys. Fluids, 14, 671 (1971)] and extend the theory to include equilibria with a central current hole.

This type of equilibrium consists of a central region with constant pressure and no poloidal magnetic field.

The equations that determine equilibria in the current hole are less singular than near the magnetic axis. All the physical quantities exist and are finite. In particular, these include the case of a current jump at the current hole boundary. Isolated equilibria with negative current in the central region could exist. But equilibria with negative currents in general do not have neighboring equilibria and thus cannot have experimental realization,

The usual hoop force balance equation,The rotational transform,The ellipticity equation,The flux renormalization equation,

An n/m = 0/1 resistive kink mode become unstable when the negative current creates a zero in the poloidal field (e. i. q is infinitive).This instability removes the negative current in the center and flattens the central current profile to zero