# Basic Plasma Physics | PPPL Theory (2022)

### Overview

Electron pressure and current for electron-beam injection into a Penning discharge
(click to enlarge).

Basic plasma theory is the exploratory study of elementary plasma phenomena and new approaches to modeling plasmas analytically and computationally. Advances in basic theory are converted into practical applications across a wide range of plasma physics research.

### Raman amplification of laser pulses using plasmas

Comparison of pulse intensities at different ampflication times (left) and output pulses (right).

Short laser pulses are useful because they can resolve transient, atomic and sub-atomic phenomena, and because they can reach ultra-high intensities. The quest for higher laser intensity and shorter pulse duration has stimulated rich study in both solid-state lasers and plasma compressors, such as backward Raman amplifiers [1,2]. The current state-of-the-art technique is represented by chirped pulse amplification [3], which can produce over $10^{14}W$ laser pulses. Further increasing pulse intensity using conventional techniques is difficult. Instead, Raman amplification of laser beams using plasma promises a breakthrough by the use of much smaller amplifying media.

Qu, Barth and Fisch [4] have proposed a novel configuration of backward Raman amplifiers by replacing the traditional counter-propagating laser seed with a plasma wave seed. This avoids issues [5] in preparing and synchronizing a frequency-shifted laser seed. They find a condition under which the plasma wave seed strictly produces the same output pulse as a counter-propagating laser seed. The advantageous, self-similar “attractor” solution can also be achieved in the longtime asymptotic limit, as shown by numerical particle-in-cell (PIC) simulations (as shown in figure, click to enlarge). Qu et al. prove that chirping the plasma wave wavelength can produce the same beneficial effects as chirping [6] the seed wave frequency.

The proposed plasma-wave-seeded Raman amplifier is comprised of an input laser pulse, called the “pump”, and a short plasma layer with a pre-existing plasma wave at one end. When the pump laser reaches the plasma wave, the Raman amplification is triggered, and this generates a counter-propagating “probe” pulse. The pump laser continuously deposits its energy into the wavefront of the probe pulse by parametrically interacting with plasma waves. The result is that almost all the pump energy is focused to the very front of the probe yielding an ultra-intense yet ultra-short laser pulse. The thermal threshold of conventional solid-state laser sources is overcome and ultra-high brilliance laser pulses are generated using the damageless property of plasmas. Full relativistic PIC simulations have shown that Raman amplifiers can generate a pulse with $~10^{18} W/cm^2$ intensity, which can reach peak intensities of $10^{25} -10^{29} W/cm^2$ after focusing.

(Video) Basic Plasma Physics 1

[1] G. Shvets, N.J. Fisch et al., Phys. Rev. Lett. 81, 4879 (1998)
[2] V.M. Malkin, G. Shvets & N.J. Fisch, Phys. Rev. Lett. 82, 4448 (1999)
[3] J. Ren, S. Li et al., Phys. Plasmas 15, 056702 (2008)
[4] Qu, Barth and Fisch, Phys. Rev. Lett. ? (2017)
[5] Z. Toroker, V.M. Malkin & N.J. Fisch, Phys. Rev. Lett. 109, 085003 (2012)
[6] Wikipedia, Chirped pulse amplification
[#h43: K. Qu, 2017-04-14]

(Video) Introduction to Plasma Physics I: Magnetohydrodynamics - Matthew Kunz

### Physics of plasma waves

Repulsion of an electromagnetic wave by a ponderomotive force on photons in modulated plasma.

Radio-frequency (RF) waves are critical not only for the heating and current drive in magnetically-confined plasmas, but also for diagnostics; however, the mathematical machinery for modeling these waves through traditional Vlasov-Maxwell theory in fusion plasmas remains antiquated.Dr. I.Y. Dodin et al. have introduced abstract mathematical methods that recognize rapid oscillations of wave fields as a distinct type of plasma dynamics with its own fundamental equations and symmetries [1].

(Video) Plasma and Plasma Physics

The development of such modernized language for wave theory, originally pursued through fundamental studies of laser-plasma interactions at Princeton University funded by the National Nuclear Security Administration (NNSA) and the Defense Threat Reduction Agency (DTRA), can now be applied with particular benefit to RF applications in tokamaks, and in other magnetic fusion devices.For example, full-wave codes could make use of the manifestly-conservative nature that the wave equations have (modulo true, physical dissipation) in their fundamental representation.It may be possible to improve the accuracy of ray-tracing codes by including the effect of polarization-driven bending of ray trajectories [2,3]; and nonlinear wave-wave interactions can be described as ponderomotive effects on photons [4], as illustrated by the figure (click to enlarge).

[1] I.Y. Dodin, Phys. Lett. A 378, 1598 (2014)

[2] D.E. Ruiz & I.Y. Dodin, Phys. Rev. A 92, 043805 (2015)
[3] D.E. Ruiz & I.Y. Dodin, Phys. Lett. A 379, 2337 (2015)
[4] I.Y. Dodin & N.J. Fisch, Phys. Rev. Lett. 112, 205002 (2014)
[#h3: I.Y. Dodin, 2016-05-23]

### Hamiltonian gyrokinetic Vlasov-Maxwell

We have found a new formulation of collisionless electromagnetic gyrokinetic theory with three novel features: (i) it is manifestly gauge invariant; (ii) the equations governing the electromagnetic field are hyperbolic in nature; and (iii) the gyrokinetic system of equations can be cast as an infinite-dimensional noncanonical Hamiltonian system [1].\begin{eqnarray}\left[ {\cal F},{\cal G}\right] & = & \sum_{s=1}^{N_s} \int {\cal B}_{s}^{gy} \left({\bf d}\frac{\delta {\cal F}}{\delta f_s} - 4 \pi e_s \frac{\delta {\cal F}}{\delta {\bf D}} \cdot d{\bf X},{\bf d}\frac{\delta {\cal G}}{\delta f_s} - 4 \pi e_s \frac{\delta {\cal G}}{\delta {\bf D}} \cdot d{\bf X}\right) f_s \\& + & 4 \pi c \int \left( \frac{\delta {\cal F}}{\delta {\bf D}} \cdot \nabla \times \frac{\delta {\cal G}}{\delta {\bf B}} -\frac{\delta {\cal G}}{\delta {\bf D}} \cdot \nabla \times \frac{\delta {\cal F}}{\delta {\bf B}}\right)d^3{\bf X}.\end{eqnarray}We have therefore succeeded in importing to gyrokinetics all of the qualitative mathematical structure contained in the “collisionless theory of everything”, which is embodied by the Vlasov-Maxwell equations. Interestingly, the new formulation supports light waves, but these propagate at the Alfvén speed instead of the speed of light. The culprit for this modification is the large effective dielectric constant in the gyrokinetic vacuum.

By leveraging the model's Hamiltonian form, we have derived an energy principle for assessing the stability of electromagnetic gyrokinetic equilibria. As a proof-of-principle calculation involving the energy principle, we have constructed the first rigorous proof that a gyrokinetic thermal equilibrium in a uniform background is stable. There is a growing need for reduced data motion and increased efficiency-to-solution in algorithms deployed on modern massively-parallel super computers. In light of this challenge, these new gyrokinetic equations offer an attractive alternative basis for large-scale gyrokinetic simulations. Due to the hyperbolic nature of the field equations, all dynamical variables in the theory can be advanced on a parallel computer in a manner that requires only nearest-neighbor, i.e. local, communication.

(Video) Plasma Physics Basics - Understanding The Fields

[1] J.W. Burby, A.J. Brizard et al., Phys. Lett. A, 379, 2073 (2015)
[#h15: H. Qin, 2016-05-23]

### High-intensity charged particle dynamics in general focusing lattice

The fundamental theoretical framework of accelerator physics is based on the Courant-Snyder (CS) theory, a theoretical description of charged particle dynamics in an alternating-gradient quadrupole focusing lattice developed by Courant & Synder in 1958 [1]; however, the CS theory can only be applied to the ideal case of an uncoupled, quadrupole focusing lattices. In realistic accelerators, there also exist “bending” magnets, torsion of the design orbit (fiducial orbit), and skew-quadrupole components introduced intentionally or by misalignment. In certain applications, solenoidal magnets are also used. When these realistic components are considered, a new theory in a higher dimension is needed.

The generalized Courant-Snyder theory published this month [2] fulfills this much-needed role. The envelope function of the original CS theory is generalized into an envelope matrix, and the phase advance is generalized into a 4D sympletic rotation (also known as the $U(2)$ group). The envelope equation, transfer matrix, and the CS invariant of the original CS theory, all have their counterparts, with remarkably similar expressions, in the generalized theory. The generalization of the 1D envelope equation (also known as the Ermakov-Milne-Pinney equation in quantum mechanics) to higher dimensions will have broad applications in various branches of physics.

To accelerate and transport high-intensity beams, it is also critical to understand in what modes the beams can propagate quiescently through an alternating-gradient focusing channel. Until now, the only known class of exactly soluble modes of intense beam propagation including self-electric and self-magnetic field effects is the Kapchinskij-Vladimirskij (KV) distribution discovered in 1959.Using the generalized CS theory, and in particular the generalized envelope equation in higher dimension, a new class of propagation modes admitted by the nonlinear Vlasov-Maxwell equations was discovered after applying the Cholesky decomposition technique [3]. The newly discovered propagation modes enable a large increase in flexibility in the amount of beam control and steering capability. For example, the new modes allow the beam to “tumble” (rotate) in the transverse plane perpendicular to the propagation direction, which can be utilized as a beam smoothing technique for accelerator applications where smooth illumination is required, such as in the case of accelerators for heavy ion fusion and medical applications.

(Video) Lecture 1 - Definition of a plasma, examples, plasma temperature, Debye shielding, plasma criteria

[1] E.D Courant & H.S Snyder, Ann. Phys. 3, 1 (1958)
[2] Hong Qin, Ronald C. Davidson et al., Phys. Rev. Lett. 111, 104801 (2013)
[3] Hong Qin & Ronald C. Davidson, Phys. Rev. Lett. 110, 064803 (2013)
[#h17: H. Qin, 2016-05-23]

## FAQs

### What is the theory of plasma? ›

Plasma is the fourth state of matter, and it is defined as “a quasineutral gas of charged and neutral particles which exhibits collective behavior.” As plasma contains charged particles, these charged particles move around and generate local concentrations of positive or negative charges (collective behavior) which ...

### What physics concepts are applied in plasma physics? ›

Plasma physics is the study of charged particles and fluids interacting with self-consistent electric and magnetic fields. It is a basic research discipline that has many different areas of application — space and astrophysics, controlled fusion, accelerator physics and beam storage.

### What is the main source of plasma in physics? ›

Most plasmas are created when extra energy is added to a gas, knocking electrons free from atoms. High temperatures often cause plasmas to form. Atoms in a hot gas are moving so fast that when they collide with each other they sometimes knock electrons loose.

### What is plasma in quantum physics? ›

plasma, in physics, an electrically conducting medium in which there are roughly equal numbers of positively and negatively charged particles, produced when the atoms in a gas become ionized. It is sometimes referred to as the fourth state of matter, distinct from the solid, liquid, and gaseous states.

### Is plasma hotter than fire? ›

Fire is just a gas that's so hot it emits light. Plasma is a gas that's so much hotter that the electrons also come loose from the atoms (and it still emits light.)

### What state of matter is plasma? ›

Plasma is often called “the fourth state of matter,” along with solid, liquid and gas. Just as a liquid will boil, changing into a gas when energy is added, heating a gas will form a plasma – a soup of positively charged particles (ions) and negatively charged particles (electrons).

### What color is plasma energy? ›

The colour comes from the fuel, which is basically hydrogen . Hydrogen gives out two different colours, a strong red and aqua-blue, which combine to give the pink colour that shows up in most pictures.

### What symbol best represents plasma? ›

The plasma approximation: The plasma approximation applies when the plasma parameter Λ, representing the number of charge carriers within the Debye sphere is much higher than unity.

### What are 3 uses of plasma? ›

Plasma is being used in many high tech industries. It is used in making many microelectronic or electronic devices such as semiconductors. It can help make features on chips for computers. Plasma is also used in making transmitters for microwaves or high temperature films.

### What is the importance of plasma physics? ›

Plasma research is leading to profound new insights on the inner workings of the Sun and other stars, and fascinating astrophysical objects such as black holes and neutron stars. The study of plasma is enabling prediction of space weather, medical treatments, and even water purification.

### What color is plasma? ›

Blood plasma is the yellow liquid component of blood, in which the blood cells in whole blood are normally suspended. The color of the plasma varies considerably from one sample to another from barely yellow to dark yellow and sometimes with a brown, orange or green tinge [Figure 1a] also.

### Is plasma A energy? ›

Plasma energy changes the world

The term plasma designates matter with a high, unstable energy level. When plasma comes into contact with solid materials like plastics and metals, its energy acts on the surfaces and changes important properties, such as the surface energy.

### Why is plasma a state of matter? ›

Plasma is a form of matter in which many of the electrons wander around freely among the nuclei of the atoms. Plasma has been called the fourth state of matter, the other three being solid, liquid and gas. Normally, the electrons in a solid, liquid, or gaseous sample of matter stay with the same atomic nucleus.

### Who discovered plasma? ›

The existence of “the fourth state of matter" was first identified by Sir William Crookes in 1879 , however, the term plasma was introduced by I. Langmuir in 1928 to describe the state of matter in the positive column of glow discharge tube [2].

### What are the two types of plasma? ›

Plasma classification (types of plasma)
• 4.1 Collisional plasma.
• 4.2 Non-collisional plasma.

### Is fire a gas or plasma? ›

Fire is a plasma, not a gas or a solid. It's a kind of transient state between being composed of the elements prior to ignition and the spent fumes (Smoke - solid particles and Gasses = Gas molecules.)

### What are the properties of plasma? ›

Like gases, plasmas have no fixed shape or volume, and are less dense than solids or liquids. But unlike ordinary gases, plasmas are made up of atoms in which some or all of the electrons have been stripped away and positively charged nuclei, called ions, roam freely.

### Which are the 7 states of matter? ›

The seven states of matter that I am investigating are Solids, Liquids, Gases, Ionized Plasma, Quark-Gluon Plasma, Bose-Einstein Condensate and Fermionic Condensate. Solid Definition - Chemistry Glossary Definition of Solid.

### What happens if you touch plasma? ›

If you touch the plasma ball, all of the electrons will go through you to the ground. You see only one big spark inside the ball where you put your hand. If you touch it long enough, you get filled with electrons and can light up a light bulb!

### Is Lava a plasma? ›

Liquid is represented by the lava. Many gasses are emitted by the lava during an eruption. Plasma may even be present, in the form of electrical discharges in the sky above the erupting volcano.
...
STATES OF MATTER IN AN ERUPTING VOLCANO
LIQUIDSSOLIDSGASES
lavarockscarbon dioxide, hydrogen sulfide, steam

### Is the universe made of plasma? ›

The universe is made of up of space plasma, the fourth state of matter. The universe is made of up of space plasma. Plasma is the word given to the fourth state of matter (solid, liquid, gas, plasma).

### How much plasma is in the universe? ›

On an astronomical scale, plasma is common. The Sun is composed of plasma, fire is plasma, fluorescent and neon lights contain plasma. "99.9 percent of the Universe is made up of plasma," says Dr.

### How was plasma discovered? ›

The existence of plasma was first discovered by Sir William Crookes in 1879 using an assembly that is today known as a “Crookes tube”, an experimental electrical discharge tube in which air is ionized by the application of a high voltage through a voltage coil.

### What is in the plasma? ›

Plasma is the clear, straw-colored liquid portion of blood that remains after red blood cells, white blood cells, platelets and other cellular components are removed. It is the single largest component of human blood, comprising about 55 percent, and contains water, salts, enzymes, antibodies and other proteins.

### Is plasma A energy? ›

Plasma energy changes the world

The term plasma designates matter with a high, unstable energy level. When plasma comes into contact with solid materials like plastics and metals, its energy acts on the surfaces and changes important properties, such as the surface energy.

### What color is plasma energy? ›

The colour comes from the fuel, which is basically hydrogen . Hydrogen gives out two different colours, a strong red and aqua-blue, which combine to give the pink colour that shows up in most pictures.

### Does plasma have a magnetic field? ›

Plasmas consist of charged particles—positive nuclei and negative electrons—that can be shaped and confined by magnetic forces. Like iron filings in the presence of a magnet, particles in the plasma will follow magnetic field lines.

### What can stop plasma? ›

Because plasmas are so hot, the only way to control them is using magnets. Electricity and magnetism are very closely related (see electromagnets). This means that moving charges, such as the electrons in a plasma, can behave as a magnet and be affected by a magnetic field.

### What is the most powerful plasma? ›

Stars are the most powerful known examples of plasma, with the ability to project heat energy and electromagnetic radiation for hundreds of millions of miles!

### Is plasma a living thing? ›

With so much water and substances dissolved in it it is non living and it is intercellular substance as it is present between the cells of the blood.

### Who found plasma physics? ›

Plasma was first identified in laboratory by Sir William Crookes. Crookes presented a lecture on what he called "radiant matter" to the British Association for the Advancement of Science, in Sheffield, on Friday, 22 August 1879.

### What state of matter is plasma? ›

Plasma is often called “the fourth state of matter,” along with solid, liquid and gas. Just as a liquid will boil, changing into a gas when energy is added, heating a gas will form a plasma – a soup of positively charged particles (ions) and negatively charged particles (electrons).

### Why is it called plasma? ›

The word "plasma," derived from the ancient Greek "to mold," had been in use in medicine and biology for some decades when American chemist and physicist Irving Langmuir (1881-1957) began experimenting on electrical discharges in gas at the General Electric Research and Development Center in upstate New York.

### What color is plasma? ›

Blood plasma is the yellow liquid component of blood, in which the blood cells in whole blood are normally suspended. The color of the plasma varies considerably from one sample to another from barely yellow to dark yellow and sometimes with a brown, orange or green tinge [Figure 1a] also.

### What are the properties of plasma? ›

Like gases, plasmas have no fixed shape or volume, and are less dense than solids or liquids. But unlike ordinary gases, plasmas are made up of atoms in which some or all of the electrons have been stripped away and positively charged nuclei, called ions, roam freely.

## Videos

1. Universe - Episode 1 - The Cosmology Quest - The Electric Universe and Plasma Physics
2. PLASMA - The Boss Of All States Of Matter | MONSTER BOX
(Monster Box)
3. Renormalization: QED to Plasma Physics
(Complexity Explorer)
4. Prof. Andrew Christlieb: Computational Plasma Physics
(Electrical and Computer Engineering at Michigan)
5. "Introduction to Plasma Physics II: Kinetics" by Matthew Kunz
6. Plasma, The Most Common Phase of Matter in the Universe
(SciShow)

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