Ion Cyclotron Resonance Heating (ICRH)

ICRH is used for creating a highly energetic population of some selected ions (a “tail” in the distribution function of these ions), which could further deliver heating to both electrons and thermal ions depending on the ratio between the critical energy and the tail temperature [3.6]. In contrast to NBI where the beam energy is limited by the energy of the NBI source, ICRH could accelerate ions up to the MeV range. In some cases, ICRH-accelerated helium ions can mimic fusion-generated alpha particles for important applications, such as developing and testing alpha particle diagnostics in a radiation-free plasma environment [3.7].

In the ICRH technique, a fast magneto-acoustic wave is launched by an external antenna with the frequency of the ion cyclotron range, which could be in resonance with the selected ions. A low field side antenna is usually used, as shown in Figure 3.2. The radio-frequency (RF) power density absorbed by the ions with mass mH and distribution function/resonating via (0 = n (0BH with the wave launched is given by [3.8]:

where RF diffusion is given by

VL is the ion velocity perpendicular to the magnetic field, BH is the ion cyclotron frequency, kL is the perpendicular wave-number of the fast wave launched, and Jn_{ (x) J„+l (x) are the Bessel functions of first kind.

The wave launched by the antenna is an elliptically polarised mode and its electric field can be decomposed as a sum of two components: the left-hand polarised component E.. which rotates in the ion direction, and the right-hand polarised component E , which counter-rotates. For n>2, the relation between these two components is approximately given by

Among the Bessel functions, only Bessel function of the zeroth order has a finite value at zero argument, 7o(0) 0. This case corresponds to n = 1 fundamental cyclotron resonance,

The best known and most widely explored hydrogen minority ICRH [3.6], which accelerates low- density H-minority population right from the thermal energy, is of the type (3.10). For higher-order resonances, n> 1, the argument of the Bessel functions in (3.8) must be non-zero. For example, in JET experiment with ICRH acceleration via third deuterium cyclotron harmonic, a “seed” energetic D beam with high VL obtained from NBI at -100 keV worked well [3.9].

For beam ions with high parallel velocity, the cyclotron resonance has a Doppler shift, the value of which could be significant,

In this case, the ions are accelerated at major radius shifted from the vertical line given by (3.10) and shown in Figure 3.2. Moreover, the topology of the drift ion orbits accelerated in such a manner can significantly differ from the usual trapped banana orbits.

Schematic representation of ICREI technique used in on-axis H-minority heating

FIGURE 3.2 Schematic representation of ICREI technique used in on-axis H-minority heating.

Figure 3.2 illustrates the geometry of ICRH for the on-axis H-minority case (3.10). In a toroidal solenoid, magnetic field at the outer side is lower than that at the inner side, and the radial gradient of the equilibrium magnetic field, B(R)~B{)/R makes the cyclotron frequency a function of major radius too. Because the wave with frequency со propagating from the antenna matches the local cyclotron frequency of H-minority ions, суВн (R), at some point inside the plasma, the cyclotron resonance cw = (0BH(R) becomes possible at this point. During the resonant interaction between the wave and the H-minority ions, an exchange of energy from the wave to the ions increases mostly perpendicular energy of the ions, which is further delivered to thermal ions and electrons via Coulomb collisions.

The advantages and disadvantages of ICRH could be summarised as follows:

Advantages of ICRH

Localised heating;

The tail temperature could be in the MeV range;

Hydrogen minority ICRH creates H-minority with E>Ecrn - it heats electrons;

Heating of thermal ions is also possible, for example, witli ’’He minority in DT plasma;

Some current drive.

Disadvantages

Antenna inside the vessel;

Relatively low power capability;

Plasma coupling may be a problem in the presence of edge-localised modes (ELMs), for example;

Power deposition area depends on the magnetic field.

Alpha Particle Heating and Burning Plasmas

Alpha particle heating in ignited plasmas will dramatically change the plasma scenario as the plasma will become an exothermic and highly non-linear medium. To approach such self-heated ignited fusion plasma, a concept of burning plasma was introduced, within which some auxiliary heating is still used for plasma control, in addition to plasma self-heating by fusion alpha particles.

The effects associated with alpha particles become increasingly significant as the ratio between the alpha particle heating power, Л<0.2 PFUS, and the auxiliary heating power, PIN, increases:

Q = PFUS/PIN= 1 - at the threshold;

Q~5 - alpha particles significantly affect plasma heating, and may excite AEs;

Q~ 10 - non-linear coupling becomes important between alpha particles, MHD events, turbulent transport, and interaction plasma-boundary;

Q>20 - dominant self-heating and transient ignition;

Q —> oo- ignition.

With all the above-mentioned effects, the problem of predicting with confidence how to maximise the alpha particle heating and, simultaneously, minimise alpha particle losses to the first wall becomes very challenging. An extended study of fast ions is being performed for solving this problem along the following directions: (1) experiments in present-day machines with fast ions produced by ICRH and NBI, which could match the ITER key dimension-less parameters /?&,t//?theniiai, VfJVA, R0 d(/?fast)/dr; (2) development of diagnostics of fast ions; and (3) theoretical analyses and numerical simulations of fast ion phenomena observed in present-day experiments, with further extrapolation to burning plasmas.

Currently, a source of the largest uncertainty in the predictions of alpha particles in burning plasmas is the possible excitation of Alfven instabilities via resonance interaction with alpha particles. The problem is in the very high energy of 3.52 MeV of alpha particles, which makes these fusiongenerated ions super-Alfvenic,

where VA is Alfven speed, and the estimates are for D:T=50:50 plasmas of the ITER machine with BT= 5.3 T. During the slowing-down process, the alpha particles pass the resonance condition

and may excite Alfven waves. The free energy source for such instability is associated w'ith the radial gradient of alpha particle pressure. The instability results in a radial re-distribution of alpha- particles changing the power deposition profile and possibly causing losses of highly energetic alphas.

 
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