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 ↓


Fusion Plasma


In the context of plasma physics and electrodynamics, fusion plasma is a state of matter where enormous amounts of energy are released through nuclear fusion reactions. These reactions occur when atomic nuclei combine and release energy according to Einstein's mass-energy equivalence principle, which is represented by the formula:

E = mc^2

In this equation, E stands for energy, m stands for mass, and c is the speed of light in a vacuum. Fusion plasma holds the key to unlocking a potential energy source that can meet the world's energy needs sustainably and efficiently.

Basically, plasma is the fourth state of matter, consisting of charged particles: ions and electrons. Unlike solids, liquids and gases, plasma has no definite shape or volume. When conditions such as temperature and pressure are sufficient for fusion reactions to take place, plasma becomes fusion plasma. This usually requires extremely high temperatures - on the order of millions of degrees Celsius - high enough to overcome the electrostatic repulsion between positively charged nuclei.

Visualization of fusion plasma

To better understand fusion plasma, consider a simplified illustration of a plasma reactor:

Fusion Core

In this diagram, the central circle represents the hot core of a fusion reactor where the plasma is confined. The lines leading to and from the core symbolize the magnetic fields used to contain the plasma, preventing it from coming into contact with the reactor walls and cooling prematurely.

Role of temperature and pressure in fusion plasma

The high temperatures in the fusion plasma are necessary to give the nuclei enough kinetic energy to overcome the Coulomb barrier – the electrostatic force that two protons experience when they come close to each other. Additionally, maintaining high pressure ensures that the particles are in close proximity, increasing the likelihood of collision and fusion.

Achieving and maintaining these conditions is one of the major challenges of controlled fusion. Fusion reactors aim to efficiently confine plasma so that these extreme conditions can be maintained over a sufficient time-frame. Fusion in stars, including our Sun, is naturally self-sustaining due to the enormous gravitational forces. Here on Earth, achieving similar conditions requires the development of specialized devices such as tokamaks and inertial confinement reactors.

Magnetic confinement: Tokamaks and stellarators

Tokamaks and stellarators are devices designed to achieve the conditions necessary for fusion through magnetic confinement. The tokamak uses a combination of toroidal and poloidal magnetic fields to create a stable, donut-shaped configuration:

Magnetic Field Plasma

In this illustration, the outer ellipse represents the toroidal magnetic field lines confining the plasma represented by the inner circle. By precisely controlling these magnetic fields, tokamaks can maintain the stability and shape of the plasma.

Stellarators use bent magnetic fields that naturally provide stability to the plasma configuration without requiring additional current within the plasma. While each design has its own challenges, tokamaks are being more widely researched because we have the ability to build them more affordably and efficiently than other designs.

Inertial confinement

Another way to obtain a fusion plasma is inertial confinement, which involves the use of laser beams or ion beams to compress a small pellet of fusion fuel to extremely high densities. Inertial confinement requires precise coordination of the beams to achieve uniform compression, preventing imperfections that lead to asymmetric collapse.

Formula representation in fusion plasma dynamics

The relationship between pressure, temperature, and plasma volume in these confined systems can be described by the plasma version of the ideal gas law:

PV = nRT

where P represents pressure, V is volume, n is the number of moles of particles, R is the ideal gas constant, and T is temperature. However, in the context of plasma, this equation needs modifications to take into account high energy particles and charge separations.

Another central thread within fusion plasmas is the Lawson criterion. It provides the conditions necessary to achieve a net energy gain from fusion reactions. The criterion states that for a fusion reactor to be viable, the following condition must be met:

nτT > (min threshold value)

where n is the particle density, τ is the energy confinement time, and T is the temperature. This gives researchers information on the parameters needed to sustain energy-producing fusion reactions.

Challenges in using fusion plasma

  • Confinement: Maintaining a stable confinement of the plasma to prevent its energy from being dissipated is challenging.
  • Energy input versus output: It is important to achieve a point where the energy output from the fusion reactions exceeds the energy input needed to sustain the reactions.
  • Materials durability: Developing materials that can withstand the extreme temperatures and radiation inside a fusion reactor is critical for long-term operation.
  • Cost: The economic feasibility of building and operating fusion reactors for large-scale deployment must be considered.

The future of fusion plasma research

Despite the challenges, progress in fusion research continues. Initiatives such as ITER (International Thermonuclear Experimental Reactor) aim to demonstrate the feasibility of fusion power on a practical scale. Fusion plasma presents an opportunity to revolutionise energy production by providing a clean, safe and abundant energy source.

In conclusion, the fields of plasma physics and electrodynamics offer a fascinating glimpse into the future of fusion plasma energy production. By understanding and overcoming the complex interactions within fusion plasmas, humanity moves closer to achieving a new era of energy sustainability.


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Fusion Plasma

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