🔆Plasma Physics Unit 11 – Magnetic Confinement Fusion

Fundamentals of Plasma Physics

• Plasma consists of ionized gas containing free electrons and positively charged ions
  • Exhibits collective behavior due to long-range electromagnetic interactions between charged particles
• Quasineutrality property maintains approximately equal densities of electrons and ions on macroscopic scales
• Debye shielding effect screens out electric fields over distances larger than the Debye length ($\lambda_D$)
• Plasma frequency ($\omega_p$) characterizes the oscillation of electrons in response to charge separation
• Coulomb collisions between charged particles lead to resistivity and energy exchange
• Magnetic fields strongly influence plasma behavior due to the Lorentz force ($\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$)
• Plasma beta ($\beta$) represents the ratio of plasma pressure to magnetic pressure

Magnetic Confinement Basics

• Magnetic confinement utilizes strong magnetic fields to confine plasma particles
• Charged particles gyrate around magnetic field lines with a gyroradius ($r_L$) and gyrofrequency ($\omega_c$)
• Particles are free to move along field lines but confined in the perpendicular direction
• Magnetic field geometry plays a crucial role in confinement effectiveness
  • Closed field lines (toroidal geometry) are necessary to prevent end losses
• Toroidal field ($B_\phi$) provides primary confinement, while poloidal field ($B_\theta$) prevents particle drifts
• Magnetic flux surfaces form nested toroidal surfaces of constant pressure
• Safety factor ($q$) describes the pitch of field lines and affects stability

Tokamak Design and Operation

• Tokamak is a toroidal magnetic confinement device for fusion plasma
• Toroidal field coils generate the main toroidal magnetic field for confinement
• Central solenoid induces a toroidal plasma current, creating a poloidal magnetic field
  • Plasma current also heats the plasma through ohmic heating
• Vertical field coils provide equilibrium and shape control of the plasma column
• Vacuum vessel contains the plasma and maintains ultra-high vacuum conditions
• Divertor region at the bottom of the vessel handles exhaust of heat and particles
  • Separatrix separates the confined plasma from the scrape-off layer (SOL)
• Plasma-facing components (first wall, limiters, divertor plates) withstand high heat and particle fluxes

Plasma Heating Methods

• Ohmic heating occurs due to plasma resistivity and induced toroidal current
  • Efficiency decreases at high temperatures due to reduced resistivity
• Neutral beam injection (NBI) involves injecting high-energy neutral particles into the plasma
  • Neutrals penetrate the magnetic field and transfer energy through collisions
• Radio frequency (RF) heating utilizes electromagnetic waves to heat the plasma
  • Ion cyclotron resonance heating (ICRH) couples energy to ions at their cyclotron frequency
  • Electron cyclotron resonance heating (ECRH) heats electrons at their cyclotron frequency
  • Lower hybrid heating (LHH) drives current and heats plasma at the lower hybrid frequency
• Alpha particle heating occurs naturally in fusion reactions as energetic alpha particles transfer energy to the plasma

Fusion Reactions and Energy Balance

• Fusion reactions combine light nuclei to form heavier nuclei, releasing energy
  • Deuterium-tritium (D-T) reaction is the most promising for fusion energy: $\mathrm{D} + \mathrm{T} \rightarrow \mathrm{^4He} (3.5\,\mathrm{MeV}) + \mathrm{n} (14.1\,\mathrm{MeV})$
• Lawson criterion defines the conditions necessary for a self-sustaining fusion reaction
  • Requires sufficient triple product of density, temperature, and confinement time ($n \tau_E T$)
• Fusion power density scales with the square of plasma density and fusion reactivity ($\langle\sigma v\rangle$)
• Energy balance in a fusion reactor involves heating power, fusion power, and loss mechanisms
  • Plasma loses energy through radiation (bremsstrahlung, line radiation) and transport (conduction, convection)
• Ignition occurs when alpha particle heating alone sustains the fusion reaction without external input
• Fusion gain factor ($Q$) represents the ratio of fusion power to external heating power

Plasma Instabilities and Control

• Plasma instabilities can disrupt confinement and limit fusion performance
  • Magnetohydrodynamic (MHD) instabilities arise from plasma macroscopic behavior
    • Kink instabilities (external and internal) are driven by current and pressure gradients
    • Tearing modes create magnetic islands that degrade confinement
  • Microinstabilities (drift waves, trapped particle modes) cause turbulent transport
• Plasma control systems are essential for maintaining stability and optimizing performance
  • Feedback control of plasma position, shape, and current profile
  • Active control of instabilities through external magnetic perturbations or localized heating/current drive
• Plasma-wall interactions and impurity control are crucial for long-pulse operation
  • Wall conditioning techniques (baking, glow discharge cleaning) minimize impurities
  • Divertor design and operation manage heat and particle exhaust

Diagnostic Techniques

• Magnetic diagnostics measure plasma current, position, and shape
  • Rogowski coils measure total plasma current
  • Magnetic probes and flux loops determine local magnetic fields and fluxes
• Interferometry and polarimetry measure plasma density and internal magnetic field structure
  • Based on the refractive index change due to plasma density
• Thomson scattering measures local electron temperature and density
  • Analyzes the spectrum of laser light scattered by plasma electrons
• Spectroscopy techniques diagnose plasma impurities, ion temperature, and rotation
  • Charge exchange recombination spectroscopy (CXRS) measures ion temperature and rotation velocity
• Bolometry measures total radiated power from the plasma
• Langmuir probes characterize plasma parameters in the edge and divertor regions
• Neutral particle analyzers measure the energy distribution of neutral atoms escaping the plasma

Current Challenges and Future Directions

• Scaling up tokamak devices to achieve net energy gain and demonstrate commercial feasibility
  • ITER aims to achieve $Q \geq 10$ and study burning plasma physics
  • DEMO projects plan to demonstrate electricity generation from fusion
• Developing advanced materials to withstand the harsh fusion environment
  • High heat and particle fluxes, neutron irradiation, and tritium retention
• Improving plasma confinement and stability through advanced tokamak concepts
  • Steady-state operation with high bootstrap current fraction
  • Optimized plasma shaping and active control of instabilities
• Exploring alternative magnetic confinement concepts beyond the tokamak
  • Stellarators, spherical tokamaks, reversed field pinches, and others
• Integrating fusion power plants with the electrical grid and fuel cycle infrastructure
  • Tritium breeding, extraction, and processing
  • Power conversion and energy storage systems
• Addressing societal and environmental aspects of fusion energy deployment
  • Public acceptance, safety, and regulatory frameworks
  • Fusion's role in sustainable energy mix and climate change mitigation