While the discussion in Sec. 4.6 and the confinement requirement suggested there, Eq.(4.12), provide some essential conceptual information about magnetically confined fusion, a sufficiently high plasma temperature has to be attained for sufficient fusion reactions to occur, Sec. 2.5. To attain this state, a neutral gas is heated and thereby ionized, as the gas kinetic temperature surmounts the respective ionization energy potentials. Upon this plasma formation, the heating process is still to be continued in order that the plasma approach the 10 keV temperature range favourable for a reasonable <Gv>. When these plasma temperatures are reached, their sustainment has to be considered. Of
the three processes mentioned, only ionization is elementary while both heating and high temperature sustainment are far more difficult.

The initial phase of a bum cycle, that is the attainment of sufficiently high temperature, as well as subsequently the sustainment of those conditions, can be accomplished by means such as the following:

(a) Resistive heating: this process involves Ohmic heating due to an electric current in the plasma.

(b) Compression: mechanical and/or magnetic forces are used to compress the plasma adiabatically and thus raise its temperature.

(c) Electromagnetic wave heating: electromagnetic waves from lasers or radiofrequency generators may be used to deposit energy in the plasma.

(d) Beam injection: neutral particles or pellets are injected and deposit their energy by collisional effects.

(e) Internal heating: charged fusion products collisionally transfer most of their birth energy to the plasma ions and electrons.

Resistive heating is based on Ohmic energy dissipation effects. The power deposited in a unit volume of a plasma by this method is given by

Pres = m2 (8.14)

where I is the current density; the parameter T| is the plasma resistivity and possesses a dependence on a number of collisional effects and is of the form

Ц~кТ’3/2 ■ (8.15)

The feature that the resistivity of a plasma decreases with increasing temperature means that Ohmic heating becomes progressively less effective at higher temperatures. Above about 1 keV, supplementary heating must be employed unless-as is possible for some system concepts-massive currents are applicable.

Compression methods of heating can be classified into two broad categories. If it occurs very rapidly-on the scale of 10’6 s or less-then it is an implosion and complex gas dynamics and shock wave considerations need to be introduced. If the compression occurs over longer intervals compared to the speed of thermal energy transfer, but still short relative to radiation losses, then the compression is adiabatic and the necessary relation

pVr = constant (8.16)

holds. Here 7 is the relevant adiabatic gas coefficient, as in Eq.(6.26).

Since a plasma consists of an aggregation of numerous moving electrical charges, it is subject to collective interactions exhibiting typical resonance effects. Therefore, coupling of high power (high frequency) waves to the plasma appears to be an effective heating mechanism. A most favourable application of such is the electromagnetic coupling via waves having the ion cyclotron frequency COg, i, Eq. (5.12). The ion motion can thus be resonantly enhanced to high kinetic energies. The irradiation by those high frequency waves is usually performed at the frequency C0gi„ or the harmonics 2cogJ, or 3cogJ (30-100 MHz depending on the magnetic field strength). The absorption of the irradiated electromagnetic energy increases with higher ion temperature Tj and can be managed most effectively by minimizing the distance between the wave antenna and the plasma edge.

Aside from this so-called ion cyclotron resonance heating (ICRH), there is, of course, also the possibility of electron cyclotron resonance heating (ECRH) which will require frequencies in the range of 28-140 GHz. Note that the specific heating of a particular plasma species may lead to a significant difference in Te and Tj; it is the latter which is to be raised for a sufficient fusion reactivity.

Beam injection, particularly neutral atoms or macro particles, has proven to be an important and effective means of heating. The mechanism of energy transfer in the plasma initially involves the conversion of the high energy neutrals into high energy ions by charge exchange and impact ionization; the resultant fast ions subsequently transfer part of their energy to the plasma ions and electrons by Coulomb collisions.

The rate at which injected fast ions transfer their kinetic energy Ef to the plasma involves two distinct components. The average energy transfer rate to electrons is approximately of the form

dE

<—>f->e~ AeNeT’e’2Ef, (8.17)

dt

while the transfer rate to ions may be approximated by

dE

~ Ai Ni Ef/2 (8.18)

dt 1

with both Ae and A, constants for the respective species and specified beam particles. Thus, at a high ion beam energy, most of the energy transfer is to electrons whereas at lower energies the thermal ions get a larger share.

We note that fusion product heating will occur due to the same collisional effect, i. e. Coulomb scattering. Hence the same energy transfer rates, as given by Eqs.(8.17) and (8.18), apply to the slowing down of the charged fast fusion products in the plasma which in turn is heated. In d-t fusion, this fusion power deposition is called alpha-heating, attributable to the charged particles released from the nuclear reaction. Very high energetic fusion products, e. g. 15 MeV protons from d-3He fusions, can as well lose energy by nuclear elastic scattering, which will result in discrete energy transfers to the plasma ions.