Fusion Plasma Parameters

The total plasma pressure is written

Let be the strength of the magnetic field that confines the plasma. It is helpful to define the dimensionless parameter [21] which measures the ratio of the plasma thermal energy density to the energy density of the magnetic field. It turns out that plasma stability considerations ensure that conventional magnetic confinement devices, such as tokamaks, cannot safely operate at beta values that exceed a few percent [59]. (See Section 1.10.)We can write

where is theThe previous four equations can be combined to give

Thus, we deduce that, in order to obtain a self-sustaining nuclear fusion reaction in a magnetic confinement device characterized by [see Equation (1.81)] and , the product of the magnetic field-strength and the plasma minor radius must exceed about 13 tesla-meters. Conventional superconducting magnet technology limits practical magnetic field-strengths in magnetic confinement devices to approximately T. Thus, to achieve nuclear fusion, such devices must have minor radii of about [55]. High-temperature superconducting magnet technology allows the practically achievable magnetic field-strength to be increased to approximately T. Thus, to achieve nuclear fusion, high-field devices need only have minor radii of about , which implies a reduction in the plasma volume by a factor of approximately 12 [14]. This is significant because the cost of a fusion experiment scales roughly as the volume of the experiment.

The rules of thumb that and , combined with Equations (1.23)–(1.25), allow us to make the estimates for the characteristic properties of a thermonuclear plasma trapped in both a low-field and a high-field magnetic confinement device that are given in Table 1.2. Note that these estimates accord well with the much more carefully worked out estimates given in References [55] and [14]. Roughly speaking, thermonuclear fusion requires a deuterium-tritium plasma with a minor radius of at least 1 meter, and an electron number density of at least particles per cubic meter, to be heated to a mean temperature of about 7 kilo-electronvolts, and the heat to be subsequently confined within the plasma for at least 1 second. The requisite strength of the confining magnetic field is at least 5 telsa.

Of course, in order for magnetic confinement to work properly, the gyro-radii of all of the charged particle species must be significantly less than the minor radius of the plasma. Obviously, the most stringent requirement is that the gyro-radii of alpha particle fusion products, , be less than the minor radius. Now,

(1.26) |