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The video above shows a simulation of the temperature of a solid target as it is heated by an intense short-pulse laser and converted to plasma. The laser enters from the left hand side and generates a flux of relativistic electrons which stream through the target and heat it to temperatures around 10 million degrees C

High Energy Density PhysicsHigh energy density physics (HEDP) covers the interactions of matter with temperatures in excess of a million degrees C°, or densities from that of liquid water (1 gram per cubic centimetre) to many times the density of solid lead. A more technical definition is any volume with an equivalent energy density of 1011 J/m3 or more, or a pressure of 1 Mbar, or 1 million times Earth’s atmospheric pressure, and above.

At these densities and energies, matter becomes plasma, also known as the fourth state of matter (the other three being solids, liquids, and gases). Plasmas are very different to the other states of matter, and support an extremely rich variety of complex physical phenomena, which makes them compelling to study. HEDP plasmas include fusion plasmas, high intensity lasers, stellar interiors, early universe plasmas, and supernovae.

High energy density physics is the focus of a small team of theorists within the Plasma Physics group at Imperial College. It includes S. J. Rose, D. Burridge and K. McLean. Many other members of the plasma physics group also work on HEDP.

Our particular research interests are listed in more detail below, but we work on some of the most challenging problems in HEDP including multi-species plasmas, self-consistent emission, absorption, and scattering of radiation, non-equilibrium plasmas, relativistic electron transport, and the physics of inertial confinement fusion.

High Energy Density Physics

Radiation in plasmas

E. Hill, S. J. Rose
The figure shows a comparison of the experimental data from Fig. 6 of Hoarty et al. HEDP 3 (2007) with the predictions of our DTA model and lineshape code. The accuracy of the line widths and heights allows a diagnosis of the temperature of the emitting Aluminium as 500eV (5.8 million Centigrade) and solid density (2.7 g cm-3).
The figure shows a comparison of the experimental data from Fig. 6 of Hoarty et al. HEDP 3 (2007) with the predictions of our DTA model and lineshape code. The accuracy of the line widths and heights allows a diagnosis of the temperature of the emitting Aluminium as 500eV (5.8 million Centigrade) and solid density (2.7 g cm-3).

High intensity and high energy lasers available at a number of laboratories allow solid density material to be heated to many millions of degrees Centigrade and lower density materials an order of magnitude hotter.  This allows us to create, for a very short time and in a very small volume, conditions analogous to the most extreme encountered in the universe.

Solid density laser plasma experiments allow material to be created in a condition similar to the centre of the Sun, and its radiative properties, in particular its opacity, to be measured.  The opacity of the material in the Sun is very important for understanding the transport of energy through it and therefore for the modelling which helps us to understand the internal mechanisms and structure of our star and by extension that of many stars in our universe.  Importantly, the material we create in the lab is directly measurable and in carefully controlled conditions, allowing the models used to calculate the stellar opacities to be calibrated.  The development of these models and their comparison with experiment has been an active interest within our group.

Many other solid density laser-plasma experiments are conducted in the research of many areas of plasma physics, and an important diagnosis of the conditions in these experiments is analysis of the emitted spectrum. We have worked on the development of a suite of atomic models ranging in detail from average atom models to DTA models using novel computational techniques in an effort to improve our diagnostic ability. An example is shown in figure 1.

Other work on subjects such as optical depth effects in plasmas and the use of the codes and concepts discussed above to model the plasmas encountered in Inertial Confinement Fusion is also performed, along with an ongoing modelling effort with other members of the Plasma Physics Group in order to integrate spectroscopic techniques with detailed simulations of the kinetics of laser-plasma interactions.

Work is also performed on the effects of radiation within a fusion capsule including double Compton scattering and other exotic effects.

At lower densities a radiation field applied to a plasma will often come to dominate the atomic kinetics and fundamentally change the physics of the plasma.  In astrophysics this is often seen, for example in the plasma surrounding High Mass X-ray Binaries and Active Galactic Nuclei.  We have investigated the use of atomic kinetics codes to model the laboratory experiments to simulate these astrophysical plasmas for many years and have proposed new experimental methods to reproduce these plasmas.

Solid density laser-plasma interactions

M. Sherlock, E. Hill, S. J. Rose

The figure shows the fast electron phase space; electrons are streaming through a solid density target from left to right at close to the speed of light. As they do so they induce large amplitude plasma waves, and their interaction with these waves leads to the modulated structures evident in the figure.We are interested in kinetic effects in high energy density plasmas relevant to intense laser-plasma interactions and inertial confinement fusion schemes. In a plasma, there may be deviations away from equilibrium on small length or time scales, or if the particles involved are very energetic. For example, the energy transferred to a plasma by ultra intense lasers is enough to generate large fluxes of relativistic electrons which stream through the plasma and set up complex electromagnetic fields. The electron motion can be strongly affected by these fields, but short-range "collisions" between particles are also important. How to correctly model these effects and use them in existing models is a challenging computational problem because of the disparate time and length scales involved and the need to correctly couple physics from multiple disciplines. We have developed a number of codes that employ direct Fokker-Planck, expansion. and particle methods in multiple dimensions to study these effects in both electrons and ions. Due to the heavy computational cost of these simulations, we write code to run on new accelerator hardware and traditional cluster supercomputers. 

The figure shows the fast electron phase space; electrons are streaming through a solid density target from left to right at close to the speed of light. As they do so they induce large amplitude plasma waves, and their interaction with these waves leads to the modulated structures evident in the figure.

Processes driving non-Maxwellian distributions

A. E. Turrell, M. Sherlock, S. J. Rose

The figure shows a non-Maxwellian tail driven in the deuterium distribution function by fusion produced alpha particles; these tails are formed by the large-angle Coulomb collisions not accounted for in other models of HEDP plasmas.This research explores the driving of non-Maxwellian distributions of particles in high energy density plasmas which are strongly collisional, or, equivalently, have few particles in a Debye sphere.

The Maxwell-Boltzmann distribution is the thermal equilibrium distribution for classical particles. As plasma relaxation timescales are inversely proportional to the Coulomb logarithm, itself a measure of the number of particles in a Debye sphere, strongly collisional plasmas cannot always be assumed to be in equilibrium. Sources of free energy, fusion reactions for example, can force distributions out of equilibrium and drastically change the fundamental properties of plasmas. In order to calculate the evolution of plasmas with free sources of energy, it is necessary to understand the effects, and causes, of non-Maxwellian distributions.

Non-Maxwellian distributions are typically short-lived, as distributions are forced toward equilibrium by collisions, and are rarely static because net transfers of energy must occur to sustain them. This makes them challenging to study with conventional approaches to plasma physics, and often a kinetic approach, in which particles are individually accounted for, is necessary.

The figure shows a non-Maxwellian tail driven in the deuterium distribution function by fusion produced alpha particles; these tails are formed by the large-angle Coulomb collisions not accounted for in other models of HEDP plasmas.

Inertial confinement fusion (ICF)

S. J. Rose, M. Sherlock, E. Hill, A. E. Turrell, O. Pike

Nuclear fusion is a process in which atoms coalesce, and form new atoms. Nuclear fusion reactions between light nuclei, such as isotopes of hydrogen, release vast quantities of energy. Just 1 gram of two isotopes of hydrogen, deuterium and tritium, fusing together release roughly the same amount of energy as burning 12 tonnes of coal.

Fusion powers all stars in the Universe, and, since the 1940s, people have dreamt of recreating fusion on Earth as a power source. It has many potential benefits, including that the fuel can be obtained from seawater, that fusion power would be carbon-free, and that we have reserves for thousands of years of energy.

The difficulty is that fusion reactions cannot happen unless extreme conditions, similar to the cores of stars, can be recreated. Nuclei cannot get close enough to fuse together unless they are in the form of a plasma, also known as the fourth state of matter. In a plasma, atoms split up into nuclei and electrons, and the nuclei have the opportunity to be brought closer enough together for fusion to happen.

Plasmas are notoriously difficult to handle and control, and the kind that is required for inertial confinement fusion has to be at temperatures in the millions of degrees Kelvin and at a hundred times the density of solid lead. Edward Teller, the nuclear physicist, famously said that controlling plasmas was like “trying to confine jelly with rubber bands.”

Inertial confinement fusion is a scheme to produce energy from fusion reactions by confining plasmas for a fraction of a second using the inertia of the plasma itself. A small fuel capsule, only a few millimetres across, is placed inside a gold box known as a ‘hohlraum’ (meaning a hollow space or cavity), which is itself placed in the centre of a large target chamber. The most powerful laser system on the planet is then fired at two holes in the ends of the hohlraum. This consists of 192 laser beams all of which must hit the right spot to within millionths of a metre, and the lasers, though they are on for only a fraction of a second, have a higher power rating than the entire US national grid.

The laser energy is converted to ultra-violet light, which is itself absorbed in the walls of the hohlraum. The gold hohlraum re-emits the energy as x-rays, which smoothly bathe the fuel capsule. The outside of the capsule is heated by the x-rays and begins to expand. A rocket effect occurs, where the outside layer of the capsule is thrown off, and the remaining fuel collapses inwards in order to conserve momentum. The density of the fuel increases as the sphere of fuel shrinks, and shockwaves launched by the incoming x-ray radiation converge on the centre of the fuel capsule.

From an initial temperature of just 18 degrees above absolute zero, the centre of the fuel capsule, the hotspot, then reaches a temperature of 60 million degrees, three times hotter than the core of the Sun. In these conditions, the hotspot becomes plasma in which fusion reactions can happen, releasing energy which moves out in a wave of fusion reactions, using up the rest of the surrounding fuel.

Several members of the plasma physics group at Imperial work on ICF, and we have strong links with Lawrence Livermore’s National Ignition Facility (NIF) in California, where the world's largest inertial confinement fusion experiment is based. It is hoped that this facility will eventually produce more energy from fusion reactions than is present in the initial laser radiation.

Although the energy released in fusion reactions at NIF has yet to match the energy originally in the laser beams, recently a record yield of 5x1015 fusion produced neutrons was announced, which suggests that the burn wave of fusion reactions is beginning to occur. This is an extremely important milestone.

Many researchers in the plasma physics group have an interest in ICF, especially through the Centre for Inertial Fusion Sciences (CIFS). Research undertaken by HEDP sub-group members which relates to ICF includes the spectroscopy of burning plasmas, the rate of energy transfer between different species in plasmas, and the way in which the highly non-equilibrium distributions of particles in burning plasmas affect the evolution of the burn wave of fusion reactions.

Correction Factors to 3-Temperature Weighted Opacity Calculations

K. McLean and S.J. Rose


The coupling of radiation to matter plays and important role in both astrophysical and experimental plasma physics. In high energy density (HED) regimes, the radiation can be so intense that is becomes the main driver in determining the atomic level occupation, kinetics and overall physics of a system.

Three-temperature (3T) models of plasmas in which the electrons, ions and radiation are treated locally and described by separate temperatures (T, Ti and T, respectively) have been used in plasma modelling for many years. Such models involve quantities known as weighted opacities. These are averaged opacities which enable an evaluation of integrated energy and flux in radiation transport models. The two weighted opacities most commonly used are the Planckian mean opacity ( κ) and the Rosseland mean opacity ( κ), defined by:

Opacities

To ease the computational power necessary to model these plasmas it is often assumed that in the evaluation of these opacities, TR T.  To quantify how incorrect this approximation is, a series of correction factor plots have been obtained, defining the factor by which the incorrect value must be multiplied by to obtain the corrected result. Figure 1 shows examples of these plots for Aluminium and Iron.

Rose_plot

Figure 1: Plots of correction factor of both weighted opacities shown for Iron, Z = 26 (top row) and Aluminium, Z = 13 (bottom row) as a function of β ≡ TR/T.  Results are shown for three electron temperatures: 0.1 keV, 0.5 keV and 1 keV.

Free Electron Relativistic Correction Factors to Excitation and Ionisation Rates in a Plasma

J. Beesley and S. J. Rose

When calculating rates of collisional excitation and ionisation the free electrons in a plasma are usually taken to follow the Maxwell-Boltzmann distribution. This means that they are treated classically, which is valid when both quantum mechanical and relativistic effects are insignificant. We have worked on accounting for relativistic effects.

If we use an empirical energy-dependent expression for the cross section, then special relativity affects our expression for total collisional excitation and ionisation rates for two reasons. First, electrons at a given energy travel at a lower velocity. Second, the electrons’ energy state occupation is changed from the Maxwell-Boltzmann to Maxwell–Jüttner.

We calculated the ratio of collisional rates calculated using special relativity to those calculated using classical mechanics. The rates were calculated from simple empirical formulas for the cross sections. The simple empirical cross sections depend on a single parameter: the threshold energy of the reaction. The ratios serve two purposes. First, they act as estimates for regimes in which accounting for special relativity is important. Second, they can be used as approximate correction factors to be applied post hoc to collisional rates calculated using classical mechanics from more sophisticated cross sections. We have found that the relativistic correction is significant in regimes potentially important to galactic intracluster media and diagnostic dopants in burning ICF plasmas.

Rose_Beesley

Figure 1: Maxwell–Boltzmann and Maxwell–Jüttner distributions plotted against reduced kinetic energy (η = ε/kT  - where ε is the electron kinetic energy), for a range of temperatures θ = kT/mc2

Matter from Light with Axions

Wei Wu, S P D Mangles and S J Rose

As the inverse of Dirac annihilation, the Breit-Wheeler process [1], the production of an electron-positron pair in the collision of two photons, is the simplest mechanism by which light can be transformed into matter. However, in the 80 years since its theoretical prediction, this process has never been observed. In 2014 we published a paper showing how that might be done with current high-power laser facilities [2] and in 2018 an experiment was conducted using this idea at the Gemini laser facility at the Rutherford Appleton Laboratory. It involved the collision of a beams of high-energy GeV photons (generated by laser accelerated electrons interaction with a high-Z target) with keV X-rays (generated by direct interaction of a laser beam with a high-Z foil). The results of that experiment are still being analysed. We are now exploring theoretically how the cross-section for the Breit-Wheeler process would be changed by processes involving hypothetical particles beyond the Standard Model (BSM), e.g., the axion. We use these results to predict departures from the expected Breit-Wheeler pair-production rate in the experiment and aim to use this to exclude some of the axion models.

[1] G Breit and J A Wheeler, Phys. Rev. 46, 1087 (1934)
[2] O J Pike et al, Nature Photonics, 8, 434 (2014)

Wu_WEI

The figure shows contours of the ratio between the cross-section for the Breit-Wheeler process mediated by a hypothetical axion and the value of the Breit-Wheeler cross-section as calculated in [1] for different values of the axion mass and the axion-electron/photon coupling.