5.2 Tokamak physics

Tokamaks are crucial in High Energy Density Physics, using magnetic fields to control fusion plasmas. These devices employ complex configurations of toroidal and poloidal fields to shape and confine hot plasma, aiming to achieve sustained fusion reactions.

Understanding tokamak physics is essential for advancing fusion energy research. From plasma heating methods to stability control and diagnostics, tokamaks present unique challenges in managing extreme conditions. Current experiments push the boundaries of fusion science, paving the way for future power plants.

Tokamak configuration

• Tokamaks represent a crucial component in the field of High Energy Density Physics, utilizing magnetic confinement to control and sustain fusion plasmas
• The configuration of a tokamak involves intricate magnetic field geometries and plasma shaping techniques to achieve optimal fusion conditions
• Understanding tokamak configuration provides insights into plasma behavior, confinement efficiency, and fusion reactor design principles

Toroidal magnetic field

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• Generated by external coils wrapped around the torus-shaped vacuum vessel
• Provides primary plasma confinement by guiding charged particles along field lines
• Strength typically ranges from 1-5 Tesla in modern tokamaks
• Decreases radially outward, following the relationship $B_T \propto \frac{1}{R}$, where R denotes major radius
• Plays crucial role in determining plasma stability and confinement properties

Poloidal magnetic field

• Created by toroidal plasma current induced through transformer action
• Combines with toroidal field to form helical magnetic field lines
• Strength typically an order of magnitude weaker than toroidal field
• Contributes to plasma equilibrium and stability by counteracting expansion forces
• Characterized by safety factor q, defined as $q = \frac{rB_T}{RB_P}$, where r denotes minor radius

Plasma confinement geometry

• Determined by combination of toroidal and poloidal magnetic fields
• Results in nested magnetic flux surfaces forming closed toroidal shape
• Plasma cross-section can be shaped (elongated, D-shaped) to improve stability and performance
• Incorporates X-point and separatrix for divertor configuration
• Utilizes magnetic field line pitch to control particle and heat transport

Plasma heating methods

• Achieving fusion-relevant temperatures in tokamaks requires multiple heating techniques
• Plasma heating methods in High Energy Density Physics aim to reach temperatures exceeding 100 million degrees Celsius
• Combination of different heating mechanisms allows for precise control of plasma temperature profiles and fusion performance

Ohmic heating

• Initial heating method utilizing plasma's electrical resistance
• Driven by induced toroidal plasma current through transformer action
• Heating power proportional to $P_{OH} = \eta J^2$, where η denotes plasma resistivity and J denotes current density
• Effectiveness decreases at higher temperatures due to reduced plasma resistivity
• Limited to temperatures around 1-2 keV in typical tokamak plasmas

Neutral beam injection

• Injects high-energy neutral atoms (typically hydrogen isotopes) into plasma
• Neutral beams ionize through collisions, transferring energy to bulk plasma
• Allows for localized heating and current drive capabilities
• Beam energies range from 50-500 keV depending on tokamak size and requirements
• Contributes to plasma rotation and fueling in addition to heating

Radio frequency heating

• Utilizes electromagnetic waves to transfer energy to plasma particles
• Includes various frequency ranges targeting different plasma resonances
  • Ion Cyclotron Resonance Heating (ICRH): 30-120 MHz
  • Electron Cyclotron Resonance Heating (ECRH): 50-170 GHz
  • Lower Hybrid Heating (LHH): 1-8 GHz
• Allows for precise power deposition control and localized heating
• Can be used for current drive and plasma stability control
• Efficiency depends on wave-particle interaction and absorption mechanisms

Plasma stability

• Maintaining plasma stability presents a significant challenge in tokamak operation
• High Energy Density Physics principles govern the complex interplay between plasma pressure, current, and magnetic fields
• Understanding and controlling plasma instabilities crucial for achieving sustained fusion conditions

MHD equilibrium

• Describes force balance between plasma pressure and magnetic forces
• Governed by Grad-Shafranov equation: $\Delta^* \psi = -\mu_0 R^2 \frac{dp}{d\psi} - F\frac{dF}{d\psi}$
• Equilibrium characterized by nested magnetic flux surfaces
• Involves balance between outward expansion forces and inward magnetic tension
• Determines plasma shape, position, and overall confinement properties

Kink instabilities

• Driven by current and pressure gradients in the plasma
• Manifest as helical deformations of the plasma column
• Classified by poloidal and toroidal mode numbers (m,n)
• External kink modes can lead to disruptions and plasma termination
• Internal kink modes associated with sawtooth oscillations and magnetic reconnection
• Stabilized through careful plasma shaping and control of safety factor profile

Ballooning modes

• Pressure-driven instabilities occurring on the outboard side of the torus
• Limit achievable plasma beta (ratio of plasma pressure to magnetic pressure)
• Characterized by high toroidal mode numbers and localized radial structure
• Growth rates increase with pressure gradient and magnetic field curvature
• Stabilized through magnetic shear and optimized pressure profile control
• Play crucial role in determining operational limits of tokamaks

Tokamak diagnostics

• Tokamak diagnostics provide essential measurements for understanding plasma behavior in High Energy Density Physics experiments
• Advanced diagnostic techniques allow for real-time monitoring and control of plasma parameters
• Combination of various diagnostic methods provides comprehensive picture of plasma properties and fusion performance

Magnetic measurements

• Utilize arrays of magnetic pickup coils and flux loops around the vacuum vessel
• Measure plasma current, position, shape, and magnetic fluctuations
• Rogowski coils determine total plasma current through Ampère's law
• Diamagnetic loops measure plasma pressure and stored energy
• Mirnov coils detect MHD instabilities and plasma oscillations
• Provide crucial input for plasma control systems and equilibrium reconstruction

Optical diagnostics

• Employ various spectroscopic and imaging techniques to study plasma properties
• Thomson scattering measures electron temperature and density profiles
• Interferometry and reflectometry determine electron density distributions
• Charge exchange recombination spectroscopy (CXRS) measures ion temperature and rotation
• Soft X-ray cameras detect internal plasma structures and MHD activity
• Bolometry measures total radiated power and impurity distributions

Neutron diagnostics

• Crucial for assessing fusion reaction rates and power production
• Neutron flux measurements determine fusion yield and plasma performance
• Neutron spectroscopy provides information on ion temperature and fuel composition
• Neutron activation techniques used for time-integrated neutron yield measurements
• Neutron cameras allow for spatially resolved fusion reaction profile measurements
• Essential for tritium accounting and fusion power demonstration experiments

Plasma-wall interactions

• Plasma-wall interactions play critical role in tokamak performance and longevity
• High Energy Density Physics principles govern complex processes at plasma-material interface
• Understanding and mitigating plasma-wall interactions crucial for achieving sustained fusion conditions

Divertor concept

• Specialized region designed to handle plasma exhaust and impurity control
• Utilizes magnetic field configuration to direct plasma-wall interactions to specific areas
• Consists of target plates, baffles, and pumping systems to remove particles and heat
• Allows for controlled plasma-surface interactions away from core plasma region
• Facilitates impurity removal and helium ash exhaust in fusion reactors
• Divertor geometry optimized for heat flux handling and neutral particle pumping

Plasma edge physics

• Encompasses complex phenomena occurring at plasma boundary
• Characterized by steep gradients in temperature, density, and electric field
• Involves interactions between plasma, neutral particles, and material surfaces
• Scrape-off layer (SOL) governs particle and heat transport to divertor region
• Edge localized modes (ELMs) cause periodic expulsion of particles and energy
• Crucial for understanding overall plasma confinement and fusion performance

Material erosion and redeposition

• Results from bombardment of plasma-facing components by energetic particles
• Physical sputtering occurs when incident particle energy exceeds surface binding energy
• Chemical erosion involves formation of volatile compounds (carbon with hydrogen)
• Eroded material can be redeposited elsewhere, leading to impurity accumulation
• Affects plasma-facing component lifetime and overall machine performance
• Material choice and surface conditioning techniques crucial for minimizing erosion

Tokamak operational regimes

• Tokamak operation encompasses various plasma regimes with distinct characteristics
• High Energy Density Physics principles govern transitions between different operational modes
• Understanding operational regimes crucial for optimizing tokamak performance and fusion power output

L-mode vs H-mode

• L-mode (Low confinement mode) characterized by moderate confinement and gradual profile changes
• H-mode (High confinement mode) exhibits improved confinement and steep edge gradients
• Transition from L-mode to H-mode occurs above critical heating power threshold
• H-mode features edge transport barrier and increased energy confinement time
• Confinement improvement factor typically 1.5-2 times higher in H-mode compared to L-mode
• H-mode operation associated with edge localized modes (ELMs) requiring careful management

Advanced tokamak scenarios

• Aim to improve plasma performance beyond standard H-mode operation
• Utilize tailored current and pressure profiles to enhance stability and confinement
• Include regimes such as hybrid scenario, steady-state scenario, and internal transport barrier (ITB) modes
• Hybrid scenario combines aspects of standard H-mode and advanced steady-state operation
• Steady-state scenarios aim for fully non-inductive current drive and continuous operation
• ITB modes feature localized regions of improved confinement in plasma core

Steady-state operation

• Focuses on achieving continuous tokamak operation without reliance on transformer action
• Requires non-inductive current drive methods (neutral beam injection, RF waves)
• Aims to maximize bootstrap current fraction for improved efficiency
• Involves careful control of current and pressure profiles for stability and performance
• Challenges include maintaining plasma purity and managing heat loads over extended periods
• Crucial for demonstrating viability of tokamaks as future fusion power plants

Fusion power production

• Fusion power production represents ultimate goal of tokamak research in High Energy Density Physics
• Involves harnessing energy released from fusion reactions to generate electricity
• Requires careful balance of plasma parameters, reactor design, and power extraction methods

Fusion reactions in tokamaks

• Primarily focus on deuterium-tritium (D-T) reaction due to highest cross-section at achievable temperatures
• D-T fusion releases 17.6 MeV energy per reaction (14.1 MeV neutron, 3.5 MeV alpha particle)
• Reaction rate depends on ion temperature, density, and confinement time (Lawson criterion)
• Alpha particles provide self-heating mechanism crucial for achieving ignition
• Other fusion reactions (D-D, D-He3) considered for advanced fuel cycles
• Fusion power density given by $P_{fusion} = n_D n_T \langle \sigma v \rangle E_{fusion}$

Tritium breeding

• Essential for fuel self-sufficiency in D-T fusion reactors
• Utilizes neutron capture reactions in lithium-containing blanket materials
• Breeding reactions: $^6Li + n \rightarrow T + ^4He$ and $^7Li + n \rightarrow T + ^4He + n$
• Tritium breeding ratio (TBR) must exceed unity for self-sustained operation
• Blanket design incorporates neutron multipliers (beryllium, lead) to enhance breeding
• Efficient tritium extraction and handling systems required for fuel cycle closure

Power extraction methods

• Convert fusion energy into usable electricity through various heat transfer mechanisms
• Blanket systems absorb neutron energy and convert it to heat
• Coolant choices include water, helium, and liquid metals (lithium, lead-lithium)
• High-temperature blanket designs aim to improve thermal efficiency
• Advanced concepts explore direct energy conversion methods for charged fusion products
• Balance between neutron shielding, tritium breeding, and power extraction crucial for reactor design

Tokamak engineering challenges

• Tokamak engineering in High Energy Density Physics involves overcoming numerous technical hurdles
• Addressing these challenges crucial for realizing practical fusion energy production
• Requires interdisciplinary approach combining plasma physics, materials science, and advanced engineering

Superconducting magnets

• Essential for generating strong magnetic fields required for plasma confinement
• Utilize low-temperature superconductors (NbTi, Nb3Sn) or high-temperature superconductors (REBCO)
• Operate at cryogenic temperatures (4K for LTS, 20-80K for HTS) requiring advanced cryogenic systems
• Design challenges include managing electromagnetic forces and quench protection
• Large-scale magnet systems require precise alignment and support structures
• Advanced magnet technologies aim to increase field strength and reduce reactor size

Vacuum vessel design

• Provides ultra-high vacuum environment for plasma confinement
• Must withstand high heat loads, neutron bombardment, and electromagnetic forces
• Incorporates numerous ports for diagnostics, heating systems, and maintenance access
• Requires careful consideration of materials (stainless steel, low-activation alloys)
• Design must accommodate thermal expansion and maintain structural integrity
• Includes first wall components directly facing the plasma (limiters, divertor plates)

Neutron shielding

• Crucial for protecting sensitive components and personnel from fusion neutrons
• Utilizes combination of materials with high neutron absorption and moderation properties
• Common shielding materials include borated water, concrete, and specialized alloys
• Design must balance shielding effectiveness with space constraints and activation concerns
• Neutronics calculations essential for optimizing shielding configuration and material selection
• Radiation-resistant diagnostics and control systems required for long-term reactor operation

Current tokamak experiments

• Current tokamak experiments push boundaries of High Energy Density Physics research
• Aim to demonstrate scientific and technological feasibility of fusion energy production
• Provide crucial insights for design and operation of future fusion power plants

ITER project overview

• International collaboration to build world's largest tokamak fusion experiment
• Located in Cadarache, France, with first plasma expected in late 2020s
• Designed to produce 500 MW of fusion power with Q ≥ 10 (fusion power gain)
• Utilizes superconducting magnets and advanced plasma control systems
• Will demonstrate integrated operation of key fusion technologies
• Serves as crucial step towards demonstrating commercial viability of fusion energy

JET and TFTR achievements

• JET (Joint European Torus) holds current record for fusion power output (16 MW)
• Demonstrated use of deuterium-tritium fuel mixture in tokamak environment
• TFTR (Tokamak Fusion Test Reactor) achieved breakeven equivalent conditions
• Both experiments provided valuable data on alpha particle physics and burning plasmas
• Contributed to development of advanced diagnostics and plasma control techniques
• Informed design choices and operational strategies for next-generation devices like ITER

Future tokamak prospects

• DEMO (Demonstration Power Plant) concepts aim to bridge gap between ITER and commercial reactors
• Compact high-field tokamaks explore potential for smaller, more economical fusion devices
• Advanced divertor concepts (snowflake, super-X) investigated for improved power handling
• Steady-state tokamak operation remains key goal for future experiments
• Integration of fusion-fission hybrid concepts explored for near-term applications
• Development of advanced materials and technologies crucial for realizing commercial fusion power