Abstract
1 Introduction
Magnetohydrodynamics (MHD) plays a fundamental role in a wide range of astrophysical phenomena, such as cooling of white dwarf stars[
In laboratory experiments, a flux density in the kilotesla region is needed to reveal the effect of -fields under the conditions of a laser-ablated high-energy-density plasma. There are several ways to generate such strong -fields with high-power lasers, including the important Biermann battery effect. In laser–plasma interaction, a toroidal -field is generated along the surface of the expanded plasma, where the gradients of electron density and temperature are noncollinear[
Laser facility | Target | Coil radius | Current | |||
---|---|---|---|---|---|---|
(kJ) | ( | (mm) | (T) | (kA) | ||
Lekko VIII[ | 0.1 | CC | 1 | 60 | 100 | |
Vulcan[ | 0.3 | Helmholtz coil | 1.25 | 7.5 | n.a. | |
Gekko XII[ | 1.5 | CC | 0.25 | 1500 | 8600 | |
Gekko XII[ | 1 | Double-U-turn | 0.3 | 60 | 82 | |
Gekko XII[ | 1 | Double-CC | 0.25 | 610 | 250 | |
LULI[ | 0.5 | CC | 0.25 | 800 | 340 | |
Omega[ | 1.25 | CC | 0.3 | 50 | 22 | |
SG-II[ | 2 | Single coil | 0.58 | 200 | 200 | |
Omega[ | 0.75 | U-shape | 0.25 | 210 | 180 |
Table 1. Laser-driven -fields.
The use of a capacitor–coil (CC) target to generate a controllable -field was proposed and realized on the Lekko VIII laser system by Daido
In the past few years, laser-driven coils have been applied in many laboratories with similar targets. Some typical results with nanosecond high-power lasers are listed in Table
2 Generation of the -field
The main mechanism of laser-driven -field generation involves two steps: establishment of an electrical potential and, as a consequence, generation of a -field by the driven current.
2.1 Establishment of a potential with the laser
First, when a laser pulse irradiates a disk, some electrons are heated. Suprathermal electrons escape from the disk surface, and a potential barrier is created[
The initial potential is dominated by the effect of the irradiating laser, although it is also affected by the disk material. To increase the initial potential, it is necessary to increase the number of escaping electrons. The number of escaping electrons, and thus their total charge, is determined by both the suprathermal electron temperature and the barrier potential . Considering a simple model and assuming a static barrier potential of , only electrons with an energy greater than can escape from the target surface. Assuming an energy distribution for the suprathermal electrons with an exponential high-energy tail of the form
2.2 Generation of the -field
With the establishment of an initial potential between the two disks, the target behaves toward the potential like a resistor–inductor () electrical circuit. The time evolution of the current can be treated using an model:
2.3 Discussion
The -field, generated by the potential and the current in the coil , is controlled by both the incident laser and the shape of the target. For example, from a comparison of the results of Daido
As well as those mentioned in the above discussion, some other models have been proposed for the study of laser-driven -fields[
3 Measurement of the -field
3.1 B-dot probe
A rapidly changing -field can be measured in many ways. One traditional method uses a pick-up coil, also known as a B-dot probe. The basic idea is to utilize Faraday’s law to measure -field fluctuations [
3.2 Optical probe
Another approach to measuring the -field involves the use of an optical diagnostic technique, such as that based on the Faraday effect. The Faraday effect is a magneto-optical phenomenon in which, when polarized light propagates through a magneto-optical medium in a -field, the plane of polarization is rotated, with the angle of rotation being proportional to the strength of the -field in the direction of propagation:
Another approach applies the Cotton–Mouton effect, which occurs when a Cotton–Mouton medium is subjected to a -field[
Additional measurements of the plasma profile, especially the electron density profile , are essential for accurate evaluation of the -field strength.
3.3 Charged-particle deflectometry
With the target normal sheath acceleration (TNSA), it is easy to obtain high-energy proton beams with a cutoff energy of tens of MeV[
As well as protons, high-energy electrons can be employed in deflectometry measurements. The energies of laser wakefield accelerated electrons can reach hundreds of MeV and even the GeV level[
4 Applications
We present here some typical applications of laser-driven coils to generate strong -fields for laboratory studies.
4.1 Low- magnetic reconnection
Magnetic reconnection is an important process in many astrophysical phenomena, including solar flares, star formation and auroras, and there have been a number of laboratory investigations based on laser–plasma interactions[
4.2 Collimation of relativistic electron beams
A collimated relativistic electron beam (REB) is useful for many applications, but the REBs produced by intense laser interaction with a solid target are usually strongly divergent. Simulations have shown that a kilotesla external -field could effectively decrease the angle of divergence of the REB[
4.3 MHD
Matsuo
5 Conclusions
The use of laser-driven coils is an important method to provide a strong -field at a sub-kilotesla to a kilotesla level. In addition to the high field strength achievable, the controllability of generation and accessibility of a secondary sample are other advantages of this scheme. The strength, space and time ranges of the -field could be further optimized depending on the desired application through appropriate choices of incident laser, target and coil shapes. This scheme could provide a new test bed for a range of laboratory applications including, but not limited to, HEDP, laboratory astrophysics, fusion research and laser particle acceleration. Many types of target have been tested under different laser conditions. There are also some other advanced designs for generation of strong -fields using short-pulse lasers, such as the snail-shaped target proposed by Korneev
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