What is an FRC?
FRC (Field-Reversed Configuration) is one of the magnetic field confinement methods for plasma. Plasma and magnetic confinement are explained in detail here.
The magnetic field structure of an FRC is shown in the figure below. A spheroidal plasma is formed within the open magnetic field lines.
A major feature of FRCs is that their beta value (β) is extremely high. The β is one of the indicators of plasma confinement efficiency. The higher the β, the more it is possible to confine high temperature and high density (high performance) plasma with a small external magnetic field (low cost).
The reason why FRCs are high-beta plasmas can be explained by the equilibrium (balance of forces) between their magnetic field configuration and pressure.
First, before discussing the FRC magnetic field configuration, we will briefly explain general torus (donut-shaped) magnetic fields, including tokamaks. In tokamaks, such as the International Thermonuclear Experimental Reactor ITER, confining magnetic fields are formed by the superposition of toroidal magnetic fields and poloidal magnetic fields. “Toroidal” refers to the direction of the large circumference of the donut, and “poloidal” refers to the direction of the small circumference (see the figure below).
As shown in the figure below, an FRC has a structure in which a general torus is laid down on its side and stretched in the direction of its central axis. The aspect ratio* is extremely low, and the hole of the donut collapses to create a spheroid-shaped confinement area.
(This is just a simple explanation of magnetic field configuration, and FRCs are not formed by this procedure.)
*) Aspect ratio: If the radius of the large circle of a torus (donut shape) is “R” and the radius of the small circle is ”a”, the ratio R/a is called the aspect ratio.
However, there is no toroidal magnetic field in FRCs. In FRCs, confinement is achieved only by the poloidal magnetic field created by the plasma current flowing in the toroidal direction. This is the reason why the β of FRCs is so high.
Let me explain this in detail. The pressure equilibrium (i.e. force balance) of magnetically confined plasma is expressed as:
∇p = j × B
where
| ∇p | gradient of plasma pressure |
|---|---|
| j | plasma current |
| B | magnetic field |
| j × B | Lorentz force. |
As mentioned above, there is no toroidal magnetic field in FRCs, and the magnetic field B (Bp in the figure below) and plasma current j (jt in the figure below) are mutually orthogonal. Therefore, from the definition of the cross product, it can be seen that the plasma pressure gradient is efficiently supported by the Lorentz force.[1] This is why FRCs have an extremely high β.
How to Form an FRC
The figure below shows an overview of the FRC equipment.
The procedure for the “Collisional Merging” method that we use, which is one of the FRC generation methods, is as follows. [2]
- Two plasmoids (clumps of plasma) are generated in the plasma generation sections installed at both ends of the vacuum chamber (i.e. plasma confinement section).
- These plasmoids are accelerated and transported mainly by magnetic pressure in the generation section and acceleration section (same principle as linear motor cars)
- Plasmoids collide and coalesce within the confinement region at relative speeds exceeding the speed of sound (several hundred km/s) to form the FRC plasma.
Advantages of FRCs
(1) Very high plasma confinement efficiency
As mentioned above, a major feature of FRCs is that it has an extremely high β (it can confine high-temperature, high-density plasma with a small external magnetic field). In fact, if we compare the β with other magnetic confinement methods, we get the following:
- Tokamak: β < 10%
- Herical：β < 10%
- Mirror：β ~ 30%
- FRC：β > 50%
This means that the strength of the confining magnetic field can be significantly reduced compared to other methods with low β.
(2) Robust stability
As explained in the previous section, “How to Form an FRC,” an FRC is formed when two plasmoids (clumps of plasma) collide and merge at supersonic speeds. To explain the formation process in more detail, immediately after two plasmoids collide, they are first compressed in the direction of the collision axis (horizontal direction in the figure below), then expanded in the radial direction (vertical direction in the figure below), and then in the axial direction, resulting in the FRC plasma is formed in a very short time of several tens of microseconds (1 microsecond = 1 millionth of a second). [2]
The fact that the magnetic field configuration is maintained and reformed autonomously without collapsing despite being accompanied by such severe disturbances indicates the robust stability of FRCs.
For example, in tokamaks, it is known that a disruption* phenomenon can occur if the vertical position of the plasma shifts by just a few percent. In other words,tokamaks are not capable of sustaining plasma through the dynamic formation process described above. This also shows the specific stability of FRCs.
*) Disruption: A phenomenon in which extremely high-temperature plasma suddenly becomes unstable and disappears immediately.
(3) Autonomous magnetic field coordination formation
The FRC’s magnetic field configuration is formed autonomously by plasma, and one of its major features is that there is no need to generate a strong confining magnetic field using an external coil. Furthermore, in addition to this high degree of autonomy, FRCs have a stabilizing effect due to high-energy ions introduced by the beam, and electric field control via external open magnetic field lines has been established, resulting in a high-performance FRC. [2]
(4) Simple devices
The FRC device is linear and does not have any structure penetrating the center of the plasma, making it very simple compared to other magnetic confinement methods (tokamak or helical). Therefore, we can expect to realize a fusion reactor that is highly maintainable and economical.
(5) Open system allows direct energy conversion
The magnetic field structure of FRCs consists of closed magnetic field lines and open magnetic field lines.
In the p-11B fusion reaction that we aim to achieve, alpha particles (helium nuclei), which are charged particles, are generated as shown in the diagram below.
Alpha particles can be extracted from the reactor core (fusion reaction area) along open magnetic field lines. The extracted high-energy alpha particles can directly convert their kinetic energy into electrical energy. In other words, since a steam turbine is not required for power generation, it is expected that power generation efficiency will be significantly improved.
Challenges of FRCs
(1) Plasma maintenance time
For many years, the challenge of FRCs has been the short plasma maintenance time. However, TAE Technologies, the American fusion startup, has succeeded in maintaining steady state through the stabilizing effect of high-energy ions introduced by the beam. [3]
(2) Characteristics different from low beta plasma
In many magnetically confined plasmas, such as tokamaks, their behavior has been understood based on Magnetohydrodynamics (MHD). On the other hand, in FRCs, the gyro radius*1 of the ions in the plasma is comparable to the scale of the plasma, so it is necessary to understand its behavior as a “kinetic plasma.” [2]
MHD cannot explain the fact that FRCs with extremely high β exist stably, even in small experimental equipment, far exceeding characteristic times such as the Alfvén time*2. Since the equilibrium and stability of many other magnetically confined plasmas can be understood using MHD, it is difficult for researchers in the plasma field to fully understand the characteristics of FRCs, and this is one of the challenges of FRCs.
On the other hand, in FRCs, which can be called kinetic plasma, favorable experimental results as a fusion reactor have been obtained, such as no anomalous transport*3 observed.
*1) Gyro radius: Ions have the property of moving while coiling around magnetic field lines. This is called “gyro motion,” and its radius is called “gyro radius.”
*2) Alfvén time: Transverse waves that propagate along the magnetic field lines of plasma are called “Alfvén waves.” The speed at which Alfvén waves travel is called “Alfvén velocity”, and Alfvén time = equipment size / Alvvén velocity. In laboratory plasma, the Alfvén time range is from several microseconds to several milliseconds. (1μs = 1 millionth of a second, 1ms = 1/1000 of a second)
*3) Anomalous transport: This refers to the degradation of confinement performance due to enhanced diffusion of energy and particles caused by turbulence generated within the plasma.
(3) Little technological accumulation globally
One of the challenges is that compared to other magnetic field confinement methods, such as tokamaks, there is little technological accumulation around the world. On the other hand, the high barrier to entry due to the unique experimental technology required can be considered an advantage as a startup.
Through collaboration and joint research with the Plasma Physics Lab at Nihon University, which has the only large-scale FRC device in Japan, and TAE Technologies in the United States, We explain various issues in development and promote the realization of advanced-fuel fusion.
While FRCs have many advantageous features as a fusion reactor, further research and development is required to make fusion energy real. We are conducting research and development toward the realization of an advanced fuel fusion reactor that takes advantage of the features of both the FRC and the magnetic mirror.
References
[1] TAKAHASHI Toshiki et al., 2. Fundamental Nature of FRC 2.1 Why is a Magnetic Configuration with 〈β〉~1 Possible?, J. Plasma Fusion Res. Vol.84, No.8 (2008),
[2] ASAI Tomohiko et al., How to Understand the Confinement and Stability in the Extremely High Beta State of an FRC, J. Plasma Fusion Res. Vol.96, No.4 (2020),
[3] H. Gota et al., Achievement of field-reversed configuration plasma sustainment via 10 MW neutral-beam injection on the C-2U device, Nucl. Fusion 59, 112009 (2019).