Scaling from today's experiments

The essential physics which enters into the prediction of plasma performance in ITER derives from two principal scalings which have been found to apply to ELMy H-mode plasmas:

• H-mode power threshold P_LH (MW), which defines the minimum fusion power:
  
           P_LH = 2.84 M^-1 B_T^0.82 n_e^0.58 R a^0.81 (rms err. 0.268)
  
  where M is the atomic mass of the plasma fuel (in AMU), B_T is the toroidal field on the plasma geometric axis (in T), n_e is the geometric average plasma electron density (10²⁰m^-3), and R and a are plasma major and minor horizontal radii (m).

• Thermal energy confinement time t_E,th (s) :
  
           t_E,th = 0.0562 H_H I_p^0.93 B_T^0.15 P^-0.69 n_e^0.41 M^0.19 R^1.97 e^0.58 k _a^0.78 ( rms err. 0.145)
  
  where H_H is a factor used to express the degree of enhancement that might be expected over the current mean prediction (i.e. it is usually 1), I_p is the plasma current (MA), B_T is the toroidal field on the plasma geometric axis (in T), P is the total net power crossing the separatrix from internal and external sources (MW), n_e is the geometric mean electron density (10¹⁹m^-3), M is the atomic mass of the plasma fuel (in AMU), R and a are plasma major and minor horizontal radii (m), and k_a = S_o/(pa²) with S_o being the plasma cross-sectional area.

A comparison of the H-mode thermal energy confinement times (vertical axis) with the scaling (horizontal axis) for a subset of ELMy data in the ITER H-mode database is shown below.

The step in performance

Existing experiments fall short of what is required for a power reactor in their fusion triple product (nTt) value. The plot below gives the range of experimental values which have been obtained in steady conditions. The best results are those of JET, with a plasma geometry similar to that of ITER. The extrapolation required from JET is between 20 to 30 in nTt.

nTt can be shown to be roughly proportional to the 3rd power of the plasma current, confinement enhancement factor H_H and plasma aspect ratio (A = R/a). Keeping the last two constant, the required increase in nTt is a factor 4, which leads to the 15 MA of ITER. At constant plasma aspect ratio and plasma safety factor (q) plasma current is proportional to the square of the plasma major radius, R. So the plasma needs to be roughly double the size of JET, i.e. ~6 m.

However the engineering of ITER is not the same as for JET. JET has warm copper coils close to the plasma, which can generate ~4 T fields at the plasma centre. ITER has cryogenic superconducting coil with considerable neutron shielding between them and the plasma, and can generate ~5 T fields at the plasma centre. Due to detailed optimisation and the use of improved analysis and modelling tools available since the design of JET, as well as a small increase in aspect ratio, the increase in plasma major radius that would be necessary has been kept to a minimum, at 6.2 m.

The choice of plasma aspect ratio of 3.1 is a compromise between the benefits of lower aspect ratio, such as lower magnetic field values and a larger margin relative to the H-mode power threshold, and those of higher aspect ratios, such as higher plasma densities. Practical considerations of maintenance access and of maintaining acceptable margins for equilibrium and vertical stability control also figure in the judgement.

One option to increase plasma performance is to increase the plasma vertical elongation. However, studies show that beyond a certain point it is hard to maintain plasma vertical position control using only the passive stabilisation of the vacuum vessel and the active stabilisation action of external poloidal field coils. Thus an elongation of k₉₅ = 1.7 (k_x ~ 1.84) has been selected.

The value of nTt in the above figure is that which would give Q~10 with levels of plasma beta (the ability of magnetic fields to confine plasma) currently achieved. In recent years, neoclassical tearing modes (NTMs) have been shown to limit the achievable normalised beta, b_N, and this instability might occur in the ITER target range of b_N ~ 1.5-2.5, leading to degradation of confinement (or disruptions). A stabilization technique for NTMs based on electron cyclotron current drive is, therefore, foreseen in ITER.

A single-null diverted equilibrium is chosen since the scaling of the H-mode threshold power is more favourable in single null, as opposed to double null, plasmas. Moreover, a double-null equilibrium which gives fully up-down symmetric divertor power loads is likely to impose unrealistic requirements on the accuracy of plasma vertical position control.

Scrape-off layer and divertor behaviour influence plasma performance in several ways, but the principal issues for ITER performance projections are the peak power to the divertor target, plasma helium fraction, and core plasma impurity content. This would limit helium fractions in ITER to levels generally below 6%.

Can ITER be smaller?

Smaller devices (i.e. lower nTt) would more attractive from the cost point of view, but provide smaller margins for Q=10, less likelihood of accessing Q > 10 and less flexibility to explore varying modes of operation. Increasing the size increases the operational domain and the margins but inevitably increases costs. The reference parameter set was selected as it offers a satisfactory margin for Q > 10 operation, has adequate flexibility and its cost satisfies the target.

How confident can performance predictions be?

An assessment has been done of the effect of uncertainties on ITER's performance and the degree of support for its planned operation from the existing database.

A complete scenario for steady-state operation with Q=5 which treats energy confinement, plasma profiles, current drive requirements, divertor performance and plasma equilibrium self-consistently and satisfies all relevant constraints is yet to be developed. Investigation of the optimum approach is one of the main aims of ITER.

Two main types of operational scenarios are under consideration for steady-state operation, with different radial profiles of shear (rate of change of helicity with distance): high current (~12 MA) with positive or shallow shear, and modest current (~8 MA) with negative shear. The high current scenario requires all the current drive power (100 MW) available for ITER, but the requirements on confinement (H_H~1.2) and beta (b_N ~3) are modest. The low current scenario requires more challenging values of confinement improvement H_H~1.5 and beta (b_N~3.2-3.5). The reference scenarios which have been used to set the design limits, are those for the low current approach.

As a means of approaching steady state operation, hybrid operation, in which a substantial fraction of the plasma current is driven by external heating and the bootstrap effect, leading to extension of the burn duration, has been evaluated.

Further information

Further information on ITER parameter choice can be found in the ITER Plant Description.