Could the large linear theta pinch be the solution for thermonuclear energy?

The magnetic confinement of an hydrogen plasma is actually a way to obtain thermonuclear energy. The will to reach nuclear fusion in a relatively small engine had led the researchers to conceive a magnetic confinement in a closed toroidal geometry. These toroidal machines, stellarators or tokamaks, generate some instabilities induced by the torsion of plasma and magnetic field. The technical solutions used on these engines for suppressing instabilities are very costly and reduce the economic interest of the fusion energy.

An economic way to avoid the instabilities of closed geometry could be an open linear geometry like linear theta pinch engines.

The confinement by linear theta pinch hopes reach thermonuclear conditions by a magnetic implosion of a linear plasma made of deuterium and tritium. An electric discharge in a coil surrounding the DT mixture ionizes the gas, creates an axial magnetic field and induces azimuthal electric currents in the plasma. The combination between electric currents and magnetic field creates an electromagnetic force that implodes and heats the plasma.

This configuration is named "Theta pinch" by contrast with the case named "Z pinch" where the confinement of plasma is assumed by an axial electric current through the plasma and an azimuthal magnetic field.

The best result of this sort of machine was reached by "Scylla" in Los Alamos Laboratory during the seventh years: length of plasma 5 m, ionic temperature 5 keV, time of confinement 5.10^-6 s, ionic density 5.10^22 ions/m3. Temperature and density were good for thermonuclear conditions but the confinement duration was too small. The confinement is limited by the loss of particles and energy by the ends of column plasma.

With an ionic temperature of 5 keV, the Lawson's criterion for D-T reaction is approximately 4.10^20 s.ions/m3 if the rate conversion of thermonuclear energy in electricity is 0.3. For reaching this step, an engine like Scylla must obtain a confinement duration of 8.10^-3 s. If we admit a linear relation between confinement duration and plasma length, the plasma must have a length of:

5 m * (8.10^-3 s) / (5.10^-6 s) = 8000 m

An article in Physical Review Letters edited in 1979 (*) describes a method to increase the confinement duration threefold. This result is reached by solid end plugs made of lithium deuteride which reduce the loss of particles and energy in the ends of plasma column. In our case, the minimum length of plasma could become:

8000 m / 3 = 2700 m

If the theta pinch engine can reach an ionic temperature of 10 keV, the Lawson's criterion for D-T reaction becomes 10^20 s.ions/m3. If the same ionic density (5.10^22 ions/m3) is reached, the minimum length of plasma column for breakeven could be:

- with free ends : 2000 m
- with LiD solid end plugs : 670 m

These scales are not absurd in regard of the dimensions of some scientific apparatus as the linear electron accelerator in Stanford (3000 m).

Some tests for checking the plasma stability during the implosion could be made with a plasma made of hydrogen and not deuterium nor tritium. A plasma made of hydrogen doesn't generate nuclear reactions so the essay could be made without nuclear protection. Between the Scylla length (5 m) and the minimum length for reaching Lawson’s criterion (some hundred meters or more), several steps could be tested with relative low cost: 20 m, 100 m.

An advantage of these theta pinch engines in regard of the toroidal machines is they could be batched. For example, if the 100 m engine is OK, it could be made in number and joined to form an engine of 200 m, 300 m, etc.

(*) : "Energy and particles confinement properties of an end-plugged, linear, theta pinch" by R. J. Commisso, R. R. Bartsch, C. A. Ekdahl, K. F. McKenna and R. E. Siemon, Physical Review Letters, Volume 43, number 6, pages 442-445.