In some of the preceding chapters we have referred to specific fusion systems and devices which are currently under extensive development. Our interest here is to examine some special system concepts deserving further examination.

15.3 Direct Energy Conversion

By way of introducing some unique possibilities for fusion energy conversion, we consider the sequence of energy transformations in a fission reactor. We recall that a fission event produces energetic and massive fission products which transfer their kinetic energy by collision to the host atoms in the fuel. This heats the fuel to elevated temperatures with the resultant thermal energy then transported to the coolant which is subsequently used to produce steam under pressure. The expanding steam causes rotation of a steam turbine which is directly connected to an electrogenerator to produce electricity for a distribution network.

As previously shown, the majority of reaction products in advanced fusion cycles (d-h, d-d) are ions. The motion of these ions constitutes a current flow which could, in principle, be converted into electrical energy. Some fusion reactors, particularly magnetic mirrors, are especially well suited for such purposes because ions leaking through the mirror ends already possess desirable directional properties. Specifically then, the direct collection of charged particles represents a transformation of the kinetic energy thereof to electrostatic potential energy which can act to sustain a current through an external load, RL. This concept is illustrated by the idealized collector shown in Fig. 16.1 where an ion beam impinges on a single plate collector held at voltage V+.

For analytical purposes we consider an ion beam with an initial angle-energy distribution such that the differential current J(|J.0,E0) gives the number of ions with direction cosine ц0 (i. e., ц0 = cos 0) and energy E0 crossing the plane at x=0 per cm2 per second per unit direction cosine and per unit energy. Then, the total beam current Jb, in units of cm’V, is given by integration over all ion energies and direction cosines:

(16.1)

energy, are turned around by the potential V+ prior to reaching the collector and thus become so-called retrogrades. Under the assumption that space-charge effects do not distort the ion trajectories significantly, the current Jc reaching the collector is given by

oo fIc(E0)

jc= J KH0,E0)dpL0dE0 (16.2)

E„=qV* №=1

where Цс(Ео) is the smallest direction cosine that an ion of initial energy E0 can have and still be collected, and V+ is the plate voltage. For simplicity, consider a parallel beam, J(p.0, E0) so that Eq.(16.2) reduces to

Jc=]j{E0)dE0 (16.3)

qV+

and the possible power generated in sustaining a load is thus

Pc = qV+ ]j{E0)dE0. (16.4)

qV+

With q and J(E0) specified by the fusion device, the operating voltage Vop should be such that the power output is maximized:

This last term requires differentiation of the lower limit of the integral leading to

J-]j{E0)dE0=-qJ(qV + ). (16.7)

Substituting this expression in Eq.(16.6) gives the following integral conditions on Vgp as the maximum power output:

4V+J(qV+)= J J(E0)dE0 . (16.8)

чК

Ль*

Note that Т|ье -> 1 as J(E0) -> J08(E0 — qV*p). For a possible mirror reactor we may take J о, Ey < E0 < E2

The maximum ion beam-to-electricity conversion thus occurs at the operating voltage V„ . The efficiency, given by the ratio of power output at V^p divided by the incident beam power, gives therefore

and assume a wide energy spread such that Ei < E2/2. The optimum voltage is then found from Eq. (16.8) to be E2/(2q), while the maximum efficiency is

% = ,, ■ Е, йЬ.. (16.11)

E2)

Thus, for the relatively narrow energy spread of Ei ~ E2/2, the efficiency is -67%, while at the other extreme, when Ei — 0, the efficiency decreases to 50%.

While the efficiency for a single plate is attractive, values exceeding 90% are possible with multiple-plate collectors, even with a wide range of beam energies. This is possible because the voltages on various plates can be set so as to efficiently intercept particles having different energies, Fig. 16.2. Efficiencies over 90% require 5 or more plates. However, a number of non-ideal effects not considered here, such as leakage currents, secondary electron emission currents and space charge effects can cause lower efficiencies in practice.

Direct collection requires extraction of a beam of charged particles from the fusion plasma. With a mirror-reactor, the escaping plasma, Fig. 16.3, is first magnetically expanded in order to convert vx energy to уц, and thus form a

directed flow of ions.

Fig. 16.2: Voltage-plate scheme for a multiple-plate collector. The particles with energies between 0 and qV i do not reach a collector but those with energies between qVN and qVN+i are collected on the N’th plate.

Fig. 16.3: Conversion of ion energy using a magnetic expander attached to a mirror reactor. The sharp bend in field lines exiting the expander is designed to separate the electrons from the ions.

Consider the idealized expander of Fig. 16.3 characterized by an entrance with an average magnetic field Bi and cross sectional area Ab and exit values of

B2 and A2. Conservation of the magnetic flux and particle flow provides the relations

BiAi = B2A2 (16.12a)

J1 Ai = J2 A2 (16.12b)

Be**1-

and the imposition of adiabatic invariance gives

After most of the particle energy is converted to Ец in the expander it is necessary to separate ions and electrons prior to collection. One technique is to sharply bend the magnetic field lines at the exit of the expander. Electrons will still be trapped on the lines while the ions, due to their larger momentum, will non-adiabatically cross field lines thus providing the desired separation. Separate collectors can be used for the ions and the electrons, which is particularly essential for the ions since they carry most of the energy.