PHD
  1. Classical mechanics  1.1. Newtonian mechanics  1.1.1. Laws of motion in Newtonian mechanics  1.1.2. Dynamics of particles and systems  1.1.3. Conservation laws  1.1.4. Central force motion  1.2. Lagrangian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Constraints and normalized coordinates  1.2.4. Noether's theorem  1.3. Hamiltonian mechanics  1.3.1. Hamilton's equations  1.3.2. Canonical conversion  1.3.3. Poisson bracket  1.3.4. Action-angle variable  1.4. Rigid body mobility  1.4.1. Rotation of rigid bodies  1.4.2. Moment of inertia tensor  1.4.3. Euler's equations in rigid body dynamics  1.4.4. Gyroscopic motion  1.5. Chaos and nonlinear dynamics  1.5.1. Stage space and attractive  1.5.2. Bifurcation and chaos theory  1.5.3. Hamiltonian Chaos  1.5.4. Lyapunov exponent
  2. Electrodynamics  2.1. Maxwell's equations  2.1.1. Gauss's law for electricity  2.1.2. Gauss's law for magnetism  2.1.3. Faraday's Law  2.1.4. Ampere's Law  2.1.5. Boundary conditions in Maxwell's equations  2.2. Electromagnetic waves  2.2.1. Wave equation  2.2.2. Polarization  2.2.3. Reflection and Refraction  2.2.4. Waveguides and resonators  2.3. Special relativity  2.3.1. Lorentz transformations  2.3.2. Relativistic energy and momentum  2.3.3. Relativistic electrodynamics  2.3.4. Minkowski spacetime  2.4. Radiation and scattering  2.4.1. Dipole radiation  2.4.2. Multipole expansion  2.4.3. Compton scattering  2.4.4. Thomson and Rayleigh scattering  2.5. Plasma Physics  2.5.1. Debye Screening  2.5.2. Magnetohydrodynamics  2.5.3. Plasma instability  2.5.4. Fusion Plasma
  3. Quantum mechanics  3.1. Foundations of quantum mechanics  3.1.1. Principles of quantum mechanics  3.1.2. Wave function and probability interpretation  3.1.3. Uncertainty principle  3.1.4. Quantum Tunneling  3.2. Schrödinger Equation  3.2.1. Time-dependent Schrödinger equation  3.2.2. Time-independent Schrödinger equation  3.2.3. Eigenvalues and eigenfunctions in the Schrödinger equation  3.2.4. Path integrals in quantum mechanics  3.3. Quantum operators  3.3.1. Commutators and observables  3.3.2. Angular momentum operator  3.3.3. Ladder Operator  3.3.4. Pauli matrices  3.4. Quantum entanglement and measurement  3.4.1. Bell's theorem  3.4.2. Quantum Teleportation  3.4.3. Quantum entanglement and quantum decoherence in measurement  3.4.4. Quantum entanglement and measurement in quantum mechanics  3.5. Relativistic quantum mechanics  3.5.1. Klein–Gordon equation  3.5.2. Dirac equation  3.5.3. Quantum field theory  3.5.4. Feynman path integral
  4. Statistical mechanics and thermodynamics  4.1. Classical thermodynamics  4.1.1. Laws of Thermodynamics  4.1.2. Carnot cycle  4.1.3. Entropy and free energy  4.1.4. Thermodynamic efficiency  4.2. Kinetic theory of gases  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Transport phenomenon  4.2.3. Mean free path  4.2.4. Non-equilibrium systems in the kinetic theory of gases  4.3. Statistical mechanics  4.3.1. Microstates and Macrostates  4.3.2. Partition function  4.3.3. Bose–Einstein and Fermi–Dirac statistics  4.3.4. Fluctuations and correlations  4.4. Phase transition  4.4.1. Important events  4.4.2. Landau theory  4.4.3. Ising model  4.4.4. Renormalization group theory
  5. Quantum field theory  5.1. Second Quantization  5.1.1. Quantum harmonic oscillator in second quantization  5.1.2. Creation and annihilation operators in second quantization  5.1.3. Path Integral in Second Quantization  5.1.4. Fock space  5.2. Quantum Electrodynamics  5.2.1. Feynman diagrams  5.2.2. Renormalization in quantum electrodynamics  5.2.3. Gauge invariance in quantum electrodynamics  5.2.4. Vacuum polarization  5.3. Quantum Chromodynamics  5.3.1. Quarks and gluons  5.3.2. Color range  5.3.3. Lattice QCD  5.3.4. Asymptotic freedom  5.4. Standard model of particle physics  5.4.1. Electroweak theory  5.4.2. Higgs mechanism  5.4.4. Grand Unified Theories
  6. General relativity and gravity  6.1. Einstein's field equations  6.1.1. Ricci tensor and scalar curvature  6.1.2. Schwarzschild solution  6.1.3. Kerr metric  6.1.4. Gravitational waves  6.2. Cosmology  6.2.1. Friedmann equation  6.2.2. Cosmic inflation  6.2.3. Dark matter and dark energy  6.2.4. Large scale structure  6.3. Black holes and wormholes  6.3.1. Event horizon in black holes and wormholes  6.3.2. Hawking radiation  6.3.3. Penrose process  6.3.4. Information paradox in black holes and wormholes
  7. Condensed matter physics  7.1. Crystal structure and lattice  7.1.1. Bravais lattices  7.1.2. Band theory in crystal structure and lattices  7.1.3. Phonons in crystal structure and lattice  7.1.4. Block's theorem  7.2. Superconductivity  7.2.1. BCS principle  7.2.2. Meissner effect  7.2.3. High Temperature Superconductor  7.2.4. Josephson effect

PHD → Electrodynamics ↓


Plasma Physics


Plasma physics is a branch of physics concerned with the study of plasma, often considered a fourth state of matter distinct from solid, liquid, and gas. The field combines aspects of classical mechanics, electromagnetism, statistical mechanics, quantum mechanics, and fluid dynamics. Plasmas are electrically conductive combinations of charged particles, neutrals, and fields exhibiting collective effects.

Understanding plasma

Plasmas are made up of charged particles: electrons and ions. Compared to gases, where atoms and molecules are neutral, plasma is where a significant number of the particles are ionized, creating interesting electrical properties. In its natural form, examples of plasma include the ionized gases found in stars like our sun, auroras, lightning, and neon lights.

Plasmas are strongly affected by electromagnetic forces because they are charged. This is often the most distinguishing feature that differentiates them from gases. Because of these forces, plasmas exhibit unique behaviors such as collective motion and wave phenomena.

Properties of plasma

The properties that define plasma include:

  • Quasi-neutrality: Even though they are composed of ions and electrons, plasmas maintain overall neutrality over large volumes. This is due to the equal density of positive and negative charges.
  • Debye Shielding: Plasma shields the electric potential over a characteristic length known as the Debye length. This concept is important to explain why plasmas are electrically neutral over considerable distances.
  • Collective behaviour: The behaviour of plasma is determined more by electromagnetic fields than by collisions between particles. This causes behaviour such as plasma waves and instabilities.

Basic equations of plasma physics

The dynamics of plasmas often obey several fundamental equations. These equations describe how fields and particles interact in a plasma.

Maxwell's equations

Maxwell's equations govern electromagnetic phenomena and play an important role in plasma physics. They can be written as:

∇ • E = ρ/ε₀
∇ • B = 0
∇ × E = -∂B/∂t
∇ × B = μ₀J + μ₀ε₀ ∂E/∂t

Where E is the electric field, B is the magnetic field, ρ is the charge density, J is the current density, ε₀ is the permittivity of free space, and μ₀ is the permeability of free space.

Continuity equation

The conservation of charge is described by the continuity equation:

∂ρ/∂t + ∇ • J = 0

This equation ensures that charge is conserved throughout the plasma.

Motion of charged particles

The motion of individual charged particles is often described by the Lorentz force equation:

F = q(E + v × B)

where F is the force on the particle, q is the charge, v is the velocity of the particle, and E and B are the electric and magnetic fields, respectively.

Visualization of plasma dynamics

To understand plasma physics, it is useful to visualize some basic dynamics. Consider the motion of charged particles in a magnetic field:

I B

Here, we depict charged particles moving in a field, demonstrating the effect of electric (E) and magnetic (B) fields on the motion of the particles. As the particles move, they spiral due to the effect of the magnetic field, illustrating the combined effect of electric and magnetic forces.

Applications of plasma physics

Plasma physics is essential in many fields and technologies:

  • Fusion energy: Controlled thermonuclear fusion has the potential to be a nearly unlimited energy source. The biggest challenge is maintaining the high temperature plasma needed for fusion reactions.
  • Astrophysical plasma: Most of the visible matter in the universe exists in the plasma state, including stars and the interstellar medium. Understanding plasma dynamics is important for models of star formation, solar flares, and cosmic phenomena.
  • Industrial applications: Plasma is used in processes such as semiconductor etching and in technologies such as plasma screens.
  • Space exploration: Plasma thrusters present a promising technology for spacecraft propulsion.

Understanding plasma waves and instabilities

A key concept in plasma physics is plasma waves and instabilities. These phenomena arise due to the tendency of plasmas to support wave propagation. The simplest is the Langmuir wave, where electrons oscillate around stationary ions:

ω² = ωp² + 3k²vₑ²

This dispersion relation shows how frequencies (ω) in a plasma are related to wave numbers (k). The plasma frequency ωp is the natural frequency at which the electrons oscillate. The term vₑ represents the thermal velocity of the electrons.

Imagine wave transmission, where the ions remain more or less stationary while the electrons oscillate, allowing the wave energy to travel through the plasma:

Plasma instabilities can also occur, which disrupt the uniformity and order of the plasma. They can be detrimental, such as in fusion devices, where they cause loss of confinement. Understanding the various instabilities, such as Rayleigh-Taylor or Kelvin-Helmholtz, helps in controlling plasmas.

Magnetohydrodynamics (MHD)

An essential theoretical framework in plasma physics is magnetohydrodynamics (MHD), which describes the macroscopic motion of plasma viewed as a fluid. MHD simplifies the full electromagnetic plasma theory by considering the bulk properties of the plasma and treating it as a conducting fluid influenced by magnetic fields.

The fundamental MHD equations include:

∂(ρv)/∂t + ∇ • (ρvv) = −∇p + j × B + F_viscous
∂B/∂t = ∇ × (v × B)
∇ • B = 0

These equations describe the conservation of momentum, the induction of magnetic fields, and the absence of magnetic monopoles. They apply to phenomena ranging from solar flares to terrestrial magnetic confinement devices.

Challenges in plasma physics

Due to the complex nature of plasma, researchers face several major challenges in understanding and using plasma effectively. For example, maintaining a stable plasma in a fusion reactor for long periods of time without losing energy is a difficult task due to complex behavior and instabilities.

Another challenge is accurately modeling plasmas, as this often requires sophisticated simulations that take into account their multi-layered nature with interactions occurring at both microscopic and macroscopic levels.

Conclusion

Plasma physics is a fascinating and vast field, with applications spanning scientific research and industrial technology. Understanding and harnessing the properties of plasma is vital to progress in energy, space exploration, and many other fields. The principles of plasma physics continue to provide insight into phenomena in both the natural environment and modern technology.


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Plasma Physics

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