|
|
| Fig. 1: Magnetic field and coil configuration in a tokamak. (Source: Wikimedia Commons) |
Controlled thermonuclear fusion is widely regarded as humanity's ideal power source, capable of producing theoretically limitless energy using light isotopes such as deuterium and tritium as fuel. As good as it sounds, however, there exist seemingly limitless technical challenges in harvesting nuclear energy that have been puzzling scientists and engineers for almost a century. These issues are largely responsible for the major push in plasma physics research since the early 1950s. [1]
There exist several schemes of fusion energy production, the most popular being magnetic confinement (MCF) and inertial confinement. One cannot simply bombard a target with deuterons in the hopes of a fusion reaction as most deuterons will lose their energy through scattering, thus dramatically lowering the likelihood of fusion. Rather, fusion is achieved through reactions between ions in a dense plasma. [1]
Here we focus on MCF, in which high-temperature plasma is confined via a strong magnetic field. The challenges of this confinement scheme stem from a simple yet highly elusive problem - it is very difficult to contain extremely hot plasma in a magnetic field. [1]
MCF is the confinement scheme of choice for the International Thermonuclear Experimental Reactor (ITER) - the most likely candidate for the first successful fusion reactor. Upon completion, it will produce around 500 MW of thermal output (ten times the input power). [2] It is based on the tokamak design (the best-researched MCF implementation) in which the magnetic field produces a so-called "toroidal pinch" of the plasma. When a central solenoid creates a toroidal current in the plasma, a poloidal magnetic field circles about the plasma. A toroidal field is also applied via coils about the reactor, thus creating a helical magnetic field as in Fig. 1. [3] Helical field lines, as opposed to purely toroidal field lines, are essential due to the differences between toroidal and cylindrical geometry. In a torus, the field is bent such that its influence is greater toward the inner wall than the outer. As such, without a helical field, the gyration of the particles becomes nonuniform and particles begin to drift vertically. [4] The helical magnetic forces keep the fuel confined within the reactor more effectively than a purely toroidal field does. However, magnetically confined plasma exhibits extremely complex turbulent behavior, so there are many other factors that can lead to the loss of fuel.
In a tokamak, the fuel plasma is heated to above 10 keV. This produces a significant population of ions in the 40-keV range - the energy required to maximize the cross section of the fusion reaction. [1] As the plasma heats up, its pressure increases, leading to the diffusion of energy toward the edges of the chamber - a process known as dispersion. This dispersion can be quantified through specific gradients (namely density and temperature). [3] The most obvious solution to reduce these gradients and increase confinement is to simply increase the magnetic field. When a charged particle, such as an electron, is placed in a magnetic field, it begins to gyrate about the field line and is thereby confined. Thus, in a simplistic sense, a greater magnetic field decreases the radius of gyration and slows diffusion across field lines. [1] However, besides the complications introduced by the extreme density and temperature of the plasma, the magnitude of the toroidal field is limited by material constraints. In ITER, the toroidal field along the plasma axis is 5.3 T, and the entire toroidal field carries about 40 GJ of energy, exerting large forces on the coils. [2] Thus, it is not necessarily economically feasible to increase field strength.
"Collisional diffusion", that is, the dispersion of energy deriving from particle collisions, is regarded as the theoretical baseline for observed diffusion phenomena. So-called "banana orbits", which occur when lower-energy particles move backwards after deflection by the stronger magnetic field near the inner wall, is an example of such an instability. [4] However, the true rate of diffusion is almost always significantly higher than what would be predicted solely via collisional effects. [5] These additional effects are frequently referred to as "anomalous diffusion" due to physicists' inability to describe them simply, despite the fact that they have been observed experimentally for decades. [4,5] They derive from the numerous violent perturbations of plasma equilibrium that occur in tokamaks. These can affect the current and pressure profiles and may even lead to complete fuel loss in some cases. [6] While many anomalous instabilities have been identified, their cause is poosly undestood. However, several potential explanations exist: (1) collisionless electron escape (and consequent ion diffusion) due to asymmetry in the magnetic coils, (2) asymmetric electric fields cause by obstacles in the plasma or chamber asymmetries, and (3) oscillating electric fields from unstable plasma waves. [1]
Compared to the issues of collisional diffusion, concerns of anomalous transport are often not negligible. Typically, they are attributed to changes in magnetic configuration at high currents. One example of an internal disruption is the "saw tooth" instability, where the density at the magnetic center of the plasma drops dramatically, leading to high heat transport in the central zone. [6] Other anomalous instabilities include tearing modes, edge-localized modes, and countless others. [3,7]
The cause for the occasionally extreme effect of these perturbations is magnetohydrodynamic turbulence. Since magnetic fields exert a force perpendicular to velocity, they can do no work and therefore cannot bring the plasma to thermodynamic equilibrium. As the confinement creates plasma gradients, instabilities occur over some threshold depending on the plasma configuration. [6] Researchers do not seek to completely eradicate these instabilities as such a goal would be physically impossible. [6] Because anomalous instabilities do not necessarily prevent confinement, one instead seeks to determine suitable operating conditions to eliminate disruptions.
When conditions are not suitable (as they are often not), the consequences are significant. Not only can instabilities destroy confinement, they can easily cause damage to plasma-facing components (PFCs) due to the escape of energetic particles. [7] Reciprocally, the consequent release of particles from the PFCs enter the plasma and cool it, increasing resistivity and therefore decreasing current density. [6] The current drop then weakens the poloidal magnetic field, leading to plasma extinction.
The described instabilities are only a small (and somewhat better-known) subset of a wide array of identified and anomalous transport causes. Evidently, there is much work to be done in the field of plasma stability in order to achieve sustainable confinement. In higher power density tokamaks such as ITER, there will undoubtedly be many other elusive physical behaviors that have cannot as of yet be experimentally studied. [7] Given that complex instabilities do not necessarily prevent confinement, however, there is good reason to be optimistic about the success of such MCF projects.
© Isaac Goodman. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, 3rd Ed. (Springer, 2015).
[2] "Summary of the ITER Final Design Report," International Atomic Energy Agency, IAEA/ITER EDA/DS/22, November 2001.
[3] R. Fitzpatrick, Tearing Mode Dynamics in Tokamak Plasmas (IOP Publishing, 2023).
[4] F. F. Chen, An Indispensable Truth: How Fusion Power Can Save the Planet (Springer, 2011).
[5] F. Boeschoten, "Review of Experiments on the Diffusion of Plasma Across a Magnetic Field," J. Nucl. Energy C 6, 339 (1964).
[6] P.-H. Rebut, "The Joint European Torus (JET)," Eur. Phys. J. H 43, 459 (2018).
[7] A. Hassanein and V. Sizyuk, "Potential Design Problems For ITER Fusion Device," Sci. Rep. 11, 2069 (2021).
