Plasma Heating Systems

In fusion reactors, multiple heating systems are combined to heat the plasma to over 100 million degrees. This chapter explains the equipment configuration and engineering characteristics of each heating method. For the physical principles of heating, see Principles of Plasma Heating.

Necessity and Overview of Heating Systems

Fusion Ignition Conditions and Heating Requirements

To achieve self-sustaining fusion reactions in a fusion reactor, the plasma must be heated to extremely high temperatures. The reaction rate of D-T fusion strongly depends on temperature, and the reaction rate coefficient $\langle\sigma v\rangle$ is expressed as a function of temperature as follows:

$$\langle\sigma v\rangle_{DT} \approx 1.1 \times 10^{-24} T_i^2 \quad [\text{m}^3/\text{s}] \quad (T_i = 10-20 \text{ keV})$$

Here, $T_i$ is the ion temperature (in keV units). The reaction rate coefficient peaks at about 13 keV (approximately 150 million degrees), and operation in this region is most efficient.

The fusion power $P_{\text{fus}}$ is given by:

$$P_{\text{fus}} = \frac{n_D n_T}{4} \langle\sigma v\rangle E_{\text{fus}} V$$

Here, $n_D$ and $n_T$ are the deuterium and tritium densities, $E_{\text{fus}} = 17.6$ MeV is the energy released per reaction, and $V$ is the plasma volume. For a 50:50 mixture with $n_D = n_T = n/2$:

$$P_{\text{fus}} = \frac{n^2}{16} \langle\sigma v\rangle E_{\text{fus}} V$$

The ignition condition (self-sustaining condition) requires that the heating power from alpha particles (3.5 MeV) produced by fusion exceeds the loss power:

$$P_\alpha = \frac{P_{\text{fus}}}{5} \geq P_{\text{loss}} = \frac{3nT}{\tau_E} V$$

Here, $\tau_E$ is the energy confinement time. From this condition, the triple product criterion, an extension of the Lawson criterion, is derived:

$$n T \tau_E > 3 \times 10^{21} \text{ m}^{-3} \cdot \text{keV} \cdot \text{s}$$

To satisfy this condition, external heating must achieve temperatures above 10 keV while confining high-density plasma for a sufficiently long time.

Scale of Heating Power

For ITER-class devices targeting fusion power $P_{\text{fus}} = 500$ MW, the required auxiliary heating power $P_{\text{aux}}$ is estimated from:

$$Q = \frac{P_{\text{fus}}}{P_{\text{aux}}}$$

For $Q = 10$ (ITER’s target), $P_{\text{aux}} = 50$ MW. Furthermore, during ignition, transport losses $P_{\text{loss}}$ and radiation losses $P_{\text{rad}}$ must be compensated, requiring high-power heating systems that satisfy:

$$P_{\text{aux}} > P_{\text{loss}} + P_{\text{rad}} - P_\alpha$$

Classification of Heating Methods

Plasma auxiliary heating methods are classified based on their physical mechanisms as follows:

Particle injection heating injects high-energy neutral particles into the plasma, which are thermalized through Coulomb collisions after charge exchange and ionization. The representative method is neutral beam injection (NBI).

Electromagnetic wave heating injects electromagnetic waves that resonate with specific particle groups in the plasma, transferring energy through resonant interactions. This is subdivided by frequency band:

Heating Method	Frequency Band	Resonance Target	ITER Frequency
ECRH/ECCD	Millimeter wave (100-200 GHz)	Electron cyclotron motion	170 GHz
ICRH/ICCD	VHF (20-100 MHz)	Ion cyclotron motion	40-55 MHz
LHCD	Microwave (1-10 GHz)	Electron Landau damping	5 GHz (future)

Each method has unique characteristics, differing in heating location, energy deposition target (electrons or ions), and current drive capability. By combining these methods, comprehensive control of plasma conditions becomes possible.

Absorption and Thermalization of Injected Power

The process by which injected power is absorbed by the plasma and converted to thermal energy differs by method.

In NBI, injected neutral particles are ionized in the plasma, and the generated fast ions are thermalized through Coulomb collisions. The thermalization time $\tau_s$ is given by:

$$\tau_s = \frac{3 m_b T_e^{3/2}}{(2\pi)^{3/2} n_e Z_b^2 e^4 \ln\Lambda} \sqrt{\frac{m_e}{2}}$$

This is typically on the order of 0.1-1 seconds, where $m_b$ and $Z_b$ are the mass and charge of the injected particles.

In RF heating, electromagnetic waves selectively transfer energy to particles satisfying the resonance condition. The absorbed power density is expressed using quasilinear theory describing wave-particle interactions:

$$P_{\text{abs}} = \int \mathbf{j} \cdot \mathbf{E}^* \, dV = \int \sigma_{\text{abs}} |\mathbf{E}|^2 \, dV$$

Here, $\sigma_{\text{abs}}$ is the absorption coefficient, which depends on plasma parameters and wave properties.

Limitations of Ohmic Heating

In tokamaks, ohmic heating (Joule heating) by the plasma current is the fundamental heating method. When plasma current $I_p$ flows, the heating power is given by:

$$P_{\text{OH}} = R_p I_p^2$$

Here, $R_p$ is the plasma resistance. The electrical resistivity of the plasma follows the Spitzer resistivity and is expressed as a function of electron temperature $T_e$:

$$\eta_{\text{Sp}} = \frac{m_e^{1/2} e^2 \ln\Lambda}{3\sqrt{2\pi}\epsilon_0^2 (k_B T_e)^{3/2}}$$

Here, $m_e$ is the electron mass, $e$ is the elementary charge, $\ln\Lambda$ is the Coulomb logarithm (typically 15-20), $\epsilon_0$ is the vacuum permittivity, and $k_B$ is the Boltzmann constant. In practical form:

$$\eta_{\text{Sp}} \approx 5.2 \times 10^{-5} \frac{Z_{\text{eff}} \ln\Lambda}{T_e^{3/2}} \quad [\Omega \cdot \mathrm{m}]$$

Here, $T_e$ is in keV units, and $Z_{\text{eff}}$ is the effective charge number. Looking at the temperature dependence:

$$\eta_{\text{Sp}} \propto T_e^{-3/2}$$

The resistivity drops rapidly at higher temperatures. This is because at high temperatures, the thermal velocity of electrons increases and the scattering cross-section by ions decreases. The plasma resistance is:

$$R_p = \frac{\eta_{\text{Sp}} \cdot 2\pi R_0}{\pi a^2}$$

where $R_0$ is the major radius and $a$ is the minor radius. The ohmic heating power density is:

$$p_{\text{OH}} = \eta_{\text{Sp}} j^2$$

where $j$ is the current density. As temperature increases, $\eta_{\text{Sp}}$ decreases, so the maximum temperature achievable by ohmic heating alone is limited to about 2-3 keV (approximately 20-35 million degrees). Auxiliary heating is essential to reach the 10 keV or higher temperatures required for fusion.

Auxiliary heating methods are broadly divided into two types: neutral beam injection (NBI) and radio frequency (RF) heating. RF heating is further classified by frequency band into electron cyclotron heating (ECRH), ion cyclotron heating (ICRH), and lower hybrid current drive (LHCD).

Neutral Beam Injection (NBI) Systems

Neutral beam injection is a method that injects high-energy neutral hydrogen atoms (or their isotopes) into the plasma, which are then ionized through charge exchange reactions and heat the plasma. Because neutral particles can cross magnetic field lines and reach the plasma core, efficient volume heating is possible.

System Configuration Overview

An NBI system consists of the following main components:

1. Ion source: Generates ions of hydrogen or its isotopes
2. Accelerator: Forms high-energy ion beam through electrostatic acceleration
3. Neutralizer cell: Converts ion beam to neutral particle beam
4. Residual ion deflection magnet: Separates un-neutralized ions
5. Beam dump: Heat-receiving plates that capture residual ions
6. Drift duct: Transports neutral beam to the plasma
7. Absolute valve: Separates tokamak vacuum from NBI vacuum

Ion Source Design

The ion source consists of a plasma generation section and an ion extraction/acceleration section.

In the plasma generation section, hydrogen gas is ionized by arc discharge or RF discharge. In bucket-type ion sources, permanent magnets are arranged around a cylindrical vessel to form a cusp magnetic field, improving plasma confinement. The magnetic field configuration produces:

$$B_{\text{cusp}} = B_0 \exp\left(-\frac{r}{\lambda}\right)$$

such magnetic field decay, where the central region is nearly field-free. Here, $\lambda$ is the magnetic field penetration length, typically a few cm.

In the ion extraction section, ions are extracted using a multi-aperture extractor. The extraction electrode configuration is as follows:

1. Plasma electrode: In contact with plasma, extracts ions
2. Extraction electrode: Applies negative potential to accelerate ions
3. Grounded electrode: Final acceleration and electron suppression

According to the Child-Langmuir law, the extraction current density $j$ is limited by:

$$j = \frac{4\epsilon_0}{9} \sqrt{\frac{2e}{M}} \frac{V^{3/2}}{d^2}$$

Here, $V$ is the extraction voltage, $d$ is the electrode gap, and $M$ is the ion mass. This equation shows that high current density requires high voltage and small electrode gap, but there are constraints from electrical breakdown.

The beam perveance is defined as:

$$P = \frac{I}{V^{3/2}}$$

To achieve optimal beam optics, the perveance must be matched to the matching condition.

Accelerator Configuration

Multi-stage electrostatic acceleration is used for ion beam acceleration. Positive ion NBI typically uses acceleration voltages of 50-150 kV, while negative ion NBI uses high voltages of 500 kV to 1 MV.

The electric field distribution in the accelerator is controlled by electrode configuration. By optimizing the equipotential line shapes, beam divergence is suppressed and good beam optics are achieved. Beam trajectories follow the equation of motion:

$$M\frac{d^2\vec{r}}{dt^2} = e\vec{E}$$

The evolution of the beam envelope is described by the envelope equation:

$$\frac{d^2 R}{dz^2} + k(z) R - \frac{K}{R} - \frac{\varepsilon^2}{R^3} = 0$$

Here, $R$ is the beam radius, $k(z)$ is the focusing strength, $K$ is the perveance parameter, and $\varepsilon$ is the emittance.

For high-voltage insulation, SF6 gas (sulfur hexafluoride) insulation has been used, but transition to vacuum insulation is progressing due to environmental concerns.

Positive Ion NBI Technology

In positive ion sources, three types of ions are extracted from hydrogen plasma: $\mathrm{H}^+$, $\mathrm{H}_2^+$, and $\mathrm{H}_3^+$. From a heating efficiency perspective, it is important to increase the ratio of atomic ions $\mathrm{H}^+$ (proton fraction).

Molecular ions dissociate after neutralization, and the energy is divided:

$$\mathrm{H}_2^+ \rightarrow \mathrm{H}_2^0 \rightarrow \mathrm{H}^0 + \mathrm{H}^0 \quad (E/2 \text{ each})$$ $$\mathrm{H}_3^+ \rightarrow \mathrm{H}_3^0 \rightarrow \mathrm{H}^0 + \mathrm{H}^0 + \mathrm{H}^0 \quad (E/3 \text{ each})$$

Low-energy components stop in the plasma periphery and do not contribute to core heating. To increase the proton fraction, discharge power density is increased to promote dissociation reactions in the plasma:

$$\mathrm{H}_2^+ + e^- \rightarrow \mathrm{H}^+ + \mathrm{H} + e^-$$

Bucket-type ion sources achieve proton fractions above 80% by confining high-density plasma with cusp magnetic field configurations.

The neutralization efficiency $\eta_n$ of positive ions strongly depends on beam energy $E$:

$$\eta_n = 1 - \exp(-\sigma_{10} n_g L) \times \frac{\sigma_{10}}{\sigma_{10} + \sigma_{01}}$$

Here, $\sigma_{10}$ is the electron capture cross-section, $\sigma_{01}$ is the electron loss cross-section, $n_g$ is the neutralizer gas density, and $L$ is the cell length.

When energy exceeds 100 keV, $\sigma_{10}$ drops sharply and neutralization efficiency falls below 30%. Therefore, negative ion NBI is necessary for large devices like ITER.

Negative Ion NBI Technology

Negative ion sources generate negative hydrogen ions $\mathrm{H}^-$, which have positive electron affinity (0.75 eV for H). Negative ions can maintain high neutralization efficiency even at high energies, making them suitable for heating large tokamaks.

There are two methods for negative ion production: volume production and surface production.

In volume production, negative ions are generated through a two-step process involving vibrationally excited molecules:

$$\mathrm{H}_2 + e_{\text{fast}}^- \rightarrow \mathrm{H}_2^*(v \geq 5) + e_{\text{slow}}^-$$ $$\mathrm{H}_2^*(v \geq 5) + e_{\text{slow}}^- \rightarrow \mathrm{H}^- + \mathrm{H}$$

High-energy electrons (10-30 eV) vibrationally excite molecules, and low-energy electrons (about 1 eV) cause dissociative electron attachment. To achieve these two types of electron energy distributions, a magnetic filter (transverse field of 50-100 G) separates the main discharge region from the extraction region.

The electron temperature reduction by the filter field is evaluated from energy balance:

$$n_e v_{Te} \frac{\partial T_e}{\partial x} = -\nu_{en} n_e (T_e - T_n)$$

In surface production, electron attachment reactions on low work function surfaces are utilized:

$$\mathrm{H}^+ + 2e^-_{\text{surface}} \rightarrow \mathrm{H}^-$$

By adding cesium (Cs), the surface work function is reduced (from 4-5 eV for pure metal to 1.5-2 eV for Cs-coated), significantly improving negative ion production efficiency:

$$\phi_{\text{eff}} = \phi_0 - e\sqrt{\frac{e E}{4\pi\epsilon_0}}$$

Optimization of Cs addition is a critical operating parameter for negative ion sources. Excess Cs causes electrical breakdown between electrodes, while insufficient Cs reduces negative ion production efficiency.

In negative ion beam extraction, removal of co-extracted electrons is an important challenge. A transverse magnetic field placed near the extraction electrode deflects electrons, which are captured by an electron dump. The target is to suppress the electron-to-negative-ion ratio $I_e/I_-$ to below 1.

Neutralizer Cell Design

The choice of neutralization method is a key factor determining the overall NBI system efficiency.

Gas neutralizer cells are the most proven method, neutralizing the beam in a cell filled with hydrogen or deuterium gas. The neutralization reaction is:

$$\mathrm{H}^- + \mathrm{H}_2 \rightarrow \mathrm{H}^0 + \mathrm{H}_2 + e^-$$

The cross-section $\sigma_{-0}$ is about $1 \times 10^{-20}$ m$^2$ for 1 MeV D$^-$.

The optimal gas density-length product (target thickness) $\Pi_{\text{opt}}$ is determined by:

$$\Pi_{\text{opt}} = n_g L_{\text{opt}} = \frac{1}{\sigma_{-0} + \sigma_{0+}} \ln\left(\frac{\sigma_{-0} + \sigma_{0+}}{\sigma_{0+}}\right)$$

Under this condition, the maximum neutralization efficiency is about 60%.

Plasma neutralizers can achieve neutralization efficiencies above 85%. They utilize electron stripping reactions from negative ions:

$$\mathrm{H}^- + e^- \rightarrow \mathrm{H}^0 + 2e^-$$

and

$$\mathrm{H}^- + \mathrm{H}^+ \rightarrow \mathrm{H}^0 + \mathrm{H}^0$$

However, several MW of power is required for plasma generation, limiting system efficiency improvement.

Photoneutralization uses laser light to strip electrons from negative ions:

$$\mathrm{H}^- + h\nu \rightarrow \mathrm{H}^0 + e^-$$

If the photon energy exceeds the electron affinity (0.75 eV), the reaction occurs, and theoretically over 95% neutralization efficiency is possible. The required laser power is estimated as:

$$P_{\text{laser}} = \frac{h\nu}{\sigma_{\text{pd}}} \cdot \frac{I_{\text{beam}}}{e} \cdot \frac{1}{\eta_{\text{opt}}}$$

Here, $\sigma_{\text{pd}}$ is the photodetachment cross-section (about $4 \times 10^{-21}$ m$^2$ at 1 eV), and $\eta_{\text{opt}}$ is the optical system efficiency.

Method	Neutralization Efficiency	Additional Power	Technology Maturity
Gas neutralization	About 60%	None	High
Plasma neutralization	About 85%	Several MW	Medium
Photoneutralization	About 95%	Laser	Under development

Beamline Design

The beamline is the section that transports the beam from the neutralizer cell to the plasma.

The residual ion deflection magnet separates un-neutralized ions (both positive and negative) from the beam. The deflection angle $\theta$ by magnetic field strength $B$ is:

$$\theta = \frac{eBL}{p} = \frac{eBL}{\sqrt{2ME}}$$

Here, $L$ is the effective magnet length, $p$ is the momentum, and $E$ is the beam energy. To deflect a 1 MeV deuterium beam by 5 degrees, a field integral of about 0.1 T$\cdot$m is required.

The residual ion dumps are water-cooled copper plates that receive the deflected positive and negative ions respectively. The heat load is:

$$q = \frac{P_{\text{ion}}}{A} = \frac{I_{\text{ion}} E}{A}$$

This can reach tens of MW/m$^2$. Active cooling designs (such as hypervapotron structures) handle these high heat loads.

In the drift duct, power density changes due to beam divergence. For a beam with divergence angle $\theta_d$ traveling drift distance $z$, the beam radius is:

$$r(z) = r_0 + z \tan\theta_d \approx r_0 + z\theta_d$$

To suppress beam re-ionization losses, residual gas pressure in the drift duct is maintained below $10^{-3}$ Pa.

At the injection port, the beam crosses the tokamak vacuum boundary. The port opening causes disturbance to the confinement magnetic field and reduction in tritium breeding ratio, so it must be minimized. In ITER, each NBI port opening area is limited to about 2 m$^2$.

ITER NBI System Specifications

The ITER NBI system is planned with the following specifications:

Item	Value
Beam particle species	$\mathrm{D}^0$ or $\mathrm{H}^0$
Beam energy	1 MeV ($\mathrm{D}^0$) / 870 keV ($\mathrm{H}^0$)
Injected power	33 MW (2 units), future 50 MW (3 additional possible)
Beam current	40 A ($\mathrm{D}^-$ beam/ion source)
Ion source current density	200 A/m$^2$
Extraction area	0.2 m$^2$ (1280 apertures)
Injection duration	3600 s (continuous)
Neutralization method	Gas neutralization
Neutralization efficiency	About 58% (D beam)
Total efficiency (wall-plug efficiency)	About 27%

The entire system measures 25 m long, 9 m wide, and 12 m tall, making it the world’s largest single injector.

Key technical features of ITER NBI include:

1. MAMuG (Multi-Aperture Multi-Gap) accelerator: Electrostatic acceleration to 1 MeV through 5 acceleration gaps
2. Large-area negative ion source: 0.6 m × 1.6 m extraction area
3. Long-pulse operation: Thermal design for 1-hour continuous operation
4. Cs injection system: Precise Cs control for stable negative ion production

Electron Cyclotron Heating (ECRH) Systems

Electron cyclotron heating injects millimeter waves tuned to the electron cyclotron frequency or its harmonics, resonantly transferring energy to electrons.

Electron Cyclotron Frequency and Resonance Conditions

The electron cyclotron frequency $f_{ce}$ is proportional to magnetic field strength $B$:

$$f_{ce} = \frac{eB}{2\pi m_e} = 28 B \quad [\text{GHz}]$$

Here, $B$ is in Tesla. For ITER’s magnetic field (5.3 T), $f_{ce} \approx 148$ GHz.

The resonance condition including relativistic corrections is:

$$\omega - k_\parallel v_\parallel = \frac{n\omega_{ce}}{\gamma}$$

Here, $\omega$ is the wave angular frequency, $k_\parallel$ is the wavenumber along the magnetic field, $v_\parallel$ is the electron velocity along the magnetic field, $n$ is the harmonic number (1, 2, …), and $\gamma$ is the relativistic factor:

$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}} = \sqrt{1 + \frac{p^2}{m_e^2 c^2}}$$

At electron temperature of 10 keV, a correction of about $\gamma \approx 1.02$ is needed.

The dispersion relation describing wave propagation in plasma is derived from the dielectric tensor of magnetized plasma. O-mode (ordinary wave) and X-mode (extraordinary wave) have different propagation characteristics.

The O-mode cutoff frequency is:

$$\omega_{\text{O,cutoff}} = \omega_{pe} = \sqrt{\frac{n_e e^2}{\epsilon_0 m_e}}$$

The X-mode right-hand cutoff frequency is:

$$\omega_{\text{R}} = \frac{\omega_{ce}}{2} + \sqrt{\frac{\omega_{ce}^2}{4} + \omega_{pe}^2}$$

The injection direction and polarization are selected so that the injected wave reaches the resonance layer without encountering a cutoff.

Gyrotron Operating Principles

A gyrotron is a vacuum electronic device that utilizes electron cyclotron resonance. An annular electron beam emitted from an electron gun rotates in a strong magnetic field generated by a superconducting solenoid coil and is converted to electromagnetic waves in a cavity resonator.

The electron gun has a structure called a magnetron injection gun (MIG), which shapes electrons emitted from a thermionic cathode into an annular beam using a combination of magnetic and electrostatic fields. Electron trajectories are described by the adiabatic approximation:

$$\mu = \frac{m_e v_\perp^2}{2B} = \text{const.}$$

Through magnetic compression, the perpendicular velocity component $v_\perp$ increases. The pitch factor:

$$\alpha = \frac{v_\perp}{v_\parallel}$$

is typically set to 1.2-1.5.

In the cavity resonator, interaction between the electron beam and electromagnetic wave modes converts the electron rotational energy to electromagnetic waves. Interaction efficiency is described by nonlinear theory:

$$\eta_{\text{el}} = 1 - \frac{\langle\gamma\rangle_{\text{out}}}{\gamma_{\text{in}}}$$

Here, $\langle\gamma\rangle_{\text{out}}$ is the average relativistic factor after interaction. Electronic efficiency is typically 30-40%.

The output window is a critical component of gyrotrons. Conventional ceramic windows had dielectric heating losses that were a barrier to 1 MW continuous operation, but this was solved by developing artificial diamond windows manufactured by CVD (chemical vapor deposition). Diamond’s dielectric loss tangent is:

$$\tan\delta_{\text{diamond}} \approx 10^{-5}$$

which is less than 1/10 of conventional materials (sapphire, silicon nitride). Additionally, thermal conductivity is:

$$\kappa_{\text{diamond}} \approx 2000 \text{ W/(m}\cdot\text{K)}$$

which is extremely high, suppressing local temperature rise.

In depressed collector gyrotrons, the residual kinetic energy of the electron beam after interaction is recovered. By setting the collector potential lower (depressed) than the main acceleration voltage:

$$\eta_{\text{total}} = \frac{\eta_{\text{el}}}{1 - (1-\eta_{\text{el}})\eta_{\text{col}}}$$

total efficiency is achieved, where $\eta_{\text{col}}$ is the collector recovery efficiency. State-of-the-art gyrotrons achieve over 50% total efficiency.

The modes excited in the cavity resonator are generally high-order TE modes. The ITER 170 GHz gyrotron uses the TE$_{32,9}$ mode. To convert this mode to a Gaussian beam, internal mode converters (Vlasov converter and phase-correcting mirrors) are used, achieving conversion efficiency over 96%.

Transmission System Design

Low-loss transmission systems are essential for transmission from gyrotron to launcher. The following technologies are used to achieve over 90% transmission efficiency over distances exceeding 100 m.

Circular corrugated waveguides are low-loss waveguides using the HE$_{11}$ mode (hybrid mode). Periodic grooves (corrugations) formed on the waveguide inner wall suppress power loss at the walls. Transmission loss is:

$$\alpha = \alpha_0 \left(\frac{a}{\lambda}\right)^{-3}$$

which decreases rapidly with increasing waveguide radius $a$. ITER uses waveguides with 63.5 mm inner diameter, with loss of about 0.02 dB/m.

Miter bends are mirror-type bends that perform 90-degree direction changes. A planar mirror is placed at 45 degrees to reflect the beam. Each bend has about 0.5% loss.

Polarizers are used to set the polarization of the injected wave to O-mode or X-mode. Grooved mirrors or rotating mirrors can generate arbitrary elliptical polarization.

To ensure overall transmission system reliability, vacuum and purge systems are installed. The waveguide interior is maintained at dry nitrogen or vacuum to prevent RF breakdown.

Launcher Design

The ECRH launcher is the final optical system that injects the transmitted millimeter-wave beam into the plasma. By controlling the injection angle, heating location and absorption efficiency are optimized.

Steerable mirrors use movable mirrors to control injection angle in real-time. Scanning in both poloidal and toroidal directions allows heating at any location in the plasma cross-section. Scanning speed is designed to respond to time constants required for MHD instability control (tens of ms).

ITER’s Upper Launcher is specifically designed for neoclassical tearing mode (NTM) stabilization. It precisely targets the $q = 3/2$ and $q = 2$ rational surfaces, suppressing modes through localized current drive. The injection angle control range is:

$$\theta_{\text{pol}} = 20° - 60°, \quad \theta_{\text{tor}} = \pm 35°$$

The Equatorial Launcher is primarily used for volume heating and central current drive.

ITER ECRH System Specifications

Item	Value
Frequency	170 GHz
Injected power	20 MW (upgradable to 40 MW)
Number of gyrotrons	24 (1 MW each)
Gyrotron efficiency	Over 50%
Transmission efficiency	Over 85%
Transmission distance	About 100 m
Polarization control	O/X mode switchable
Injection duration	Continuous (3600 s)

A characteristic of ECRH is that because the wavelength is short (about 1.8 mm), localized heating is possible, making it effective for MHD instability control such as neoclassical tearing modes.

Ion Cyclotron Heating (ICRH) Systems

Ion cyclotron heating injects electromagnetic waves tuned to the ion cyclotron frequency or its harmonics, directly heating ions.

Ion Cyclotron Frequency and Heating Mechanisms

The ion cyclotron frequency $f_{ci}$ is determined by ion species and magnetic field strength:

$$f_{ci} = \frac{ZeB}{2\pi M} \approx 15.2 \frac{Z}{A} B \quad [\text{MHz}]$$

Here, $Z$ is the charge number, $A$ is the mass number, and $B$ is in Tesla. For ITER’s magnetic field (5.3 T), deuterium is about 40 MHz and tritium is about 27 MHz.

Heating modes are classified as follows:

Fundamental harmonic heating ($\omega = \omega_{ci}$): Efficiency is low for single-ion-species plasmas, but efficient heating is possible using minority ion species. Heating power depends on minority ion concentration $n_{\min}/n_e$, with an optimal value around 3-10%:

$$P_{\text{abs}} \propto \left(\frac{n_{\min}}{n_e}\right) \left|E^+\right|^2$$

Here, $E^+$ is the left-hand polarized electric field component.

Harmonic heating ($\omega = n\omega_{ci}$, $n = 2, 3, ...$): Second harmonic heating is effective for direct heating of D-T plasmas. Absorption occurs through finite Larmor radius effects:

$$P_{\text{abs}} \propto (k_\perp \rho_i)^{2(n-1)} \left|E^+\right|^2$$

Here, $\rho_i$ is the ion Larmor radius.

Mode conversion heating: Conversion to ion Bernstein waves occurs in the plasma, enabling efficient electron heating.

RF Sources (Tetrodes)

For the ion cyclotron frequency band (25-55 MHz), externally excited multi-stage amplifier circuits using tetrodes (four-electrode vacuum tubes) are used. This frequency band has established technology from broadcasting, enabling reliable power amplification.

A tetrode consists of a cathode, first grid (control grid), second grid (screen grid), and anode. The amplifier generally has the following stage configuration:

1. Solid-state driver (several kW)
2. Intermediate amplification stage (tens of kW)
3. Final stage tetrode (2-3 MW)

The final stage tetrode operates in class B or class AB amplification to suppress anode dissipation. The DC-to-RF conversion efficiency is:

$$\eta_{\text{RF}} = \frac{P_{\text{RF}}}{P_{\text{DC}}} \approx 60-70\%$$

Vapor cooling is employed to efficiently remove anode heat.

ITER tetrode specifications are: frequency 40-55 MHz, single-tube output 2.5 MW, continuous operation 3600 seconds.

Matching Circuits

Impedance matching between RF sources and plasma load is essential for efficient power transfer. Since plasma load impedance varies with plasma parameters, variable matching circuits are required.

For coaxial transmission lines, the impedance is:

$$Z_0 = \frac{1}{2\pi} \sqrt{\frac{\mu}{\epsilon}} \ln\left(\frac{b}{a}\right) \approx 60 \ln\left(\frac{b}{a}\right) \quad [\Omega]$$

Here, $a$ is the inner conductor radius and $b$ is the outer conductor inner diameter.

Matching circuits generally use stub tuner or liquid stub configurations. In liquid stubs, the liquid level position in a coaxial line is varied to adjust reactance:

$$X = Z_0 \tan(kl)$$

Here, $k$ is the wavenumber and $l$ is the stub length.

The coupling resistance $R_c$ represents power coupling from antenna to plasma:

$$P_{\text{coupled}} = \frac{1}{2} R_c |I_{\text{strap}}|^2$$

Typical values are $R_c = 2-10$ $\Omega$/strap.

Fast feedback matching systems track plasma condition changes (such as ELMs) within 1 ms, suppressing reflected power.

Loop Antenna Design

ICRH antennas are installed on the low-field side (outboard) of the torus and excite fast waves in the plasma.

The antenna structure consists of radiating straps (conductor strips) and Faraday shields. Radiating straps are arranged in the poloidal direction and excite RF magnetic field components perpendicular to the toroidal field.

The fast wave dispersion relation is:

$$n_\perp^2 = \frac{(R - n_\parallel^2)(L - n_\parallel^2)}{S - n_\parallel^2}$$

Here, $R$, $L$, $S$ are the Stix parameters of the dielectric tensor, and $n_\parallel = ck_\parallel/\omega$, $n_\perp = ck_\perp/\omega$ are refractive indices.

For current drive, multiple straps are arranged toroidally with phase differences to excite a traveling wave spectrum. The toroidal wavenumber spectrum is controlled by:

$$k_\phi = \frac{\Delta\phi}{d}$$

Here, $\Delta\phi$ is the inter-strap phase difference and $d$ is the strap spacing.

The Faraday shield is an array of conductor rods arranged toroidally that suppresses unwanted electric field components (particularly those coupling to slow waves). This reduces RF sheath voltage at the plasma periphery and suppresses impurity release.

Sheath potential is evaluated as:

$$V_{\text{sh}} \approx \frac{T_e}{e} \ln\left(\frac{m_i}{2\pi m_e}\right) + \frac{|V_{\text{RF}}|}{2}$$

Ions accelerated by RF sheaths sputter wall materials, causing impurity contamination of the plasma.

Thermal design of antennas is also a critical issue. Heat loads on antenna surfaces from plasma radiation, particle flux, and RF losses reach several MW/m$^2$. This is addressed by combining active and radiative cooling.

ITER ICRH System Specifications

Item	Value
Frequency	40-55 MHz
Injected power	20 MW (upgradable to 40 MW)
RF sources	8 tetrodes, single-tube output 2.5 MW
Antennas	2 ports, each port 4×3 straps
Coupling distance	10-15 cm
Injection duration	Continuous (3600 s)
Power density	About 8 MW/m$^2$ (antenna aperture)

The antenna has a triplet array of 4 straps toroidally and 3 rows poloidally. Phase control allows switching the $k_\phi$ spectrum between +90°, 0°, -90° (dipole, monopole).

Lower Hybrid Current Drive (LHCD) Systems

Lower hybrid heating/current drive uses electromagnetic waves in the GHz band primarily for current drive. It uses frequencies near the geometric mean of the ion cyclotron frequency and ion plasma frequency.

Lower Hybrid Frequency and Wave Propagation

The lower hybrid frequency $\omega_{LH}$ is approximated by:

$$\omega_{LH}^2 = \frac{\omega_{pi}^2 + \omega_{ci}^2}{1 + \omega_{pe}^2/\omega_{ce}^2}$$

In the high-density limit ($\omega_{pe} \gg \omega_{ce}$):

$$\omega_{LH} \approx \sqrt{\omega_{ci}\omega_{ce}} = \omega_{ci}\sqrt{\frac{m_i}{m_e}}$$

For ITER plasma, this is on the order of several GHz.

Lower hybrid waves propagate as slow waves and must satisfy the accessibility condition:

$$n_\parallel > n_{\parallel,\text{acc}} = 1 + \frac{\omega_{pe}}{\omega_{ce}}$$

Here, $n_\parallel = ck_\parallel/\omega$ is the parallel refractive index.

Wave energy is absorbed by electron Landau damping. The damping condition is:

$$v_\phi = \frac{\omega}{k_\parallel} \approx 3 v_{Te}$$

Strong absorption occurs when the phase velocity is about 3 times the electron thermal velocity.

At high plasma temperatures, $v_{Te}$ increases, so Landau damping occurs at the plasma periphery, making penetration to the core difficult. This phenomenon is called the “spectral gap problem”:

$$n_\parallel = \frac{c}{v_\phi} \approx \frac{c}{3v_{Te}} = \frac{c}{3}\sqrt{\frac{m_e}{2k_BT_e}}$$

At $T_e = 10$ keV, $n_\parallel \approx 1.5$ is required, but compatibility with the accessibility condition is difficult.

Klystrons

Klystrons are used as RF sources for the lower hybrid frequency band (3-8 GHz). Klystrons are linear amplifier tubes using electron beams, developed from radar technology.

A klystron consists of an electron gun, input cavity, intermediate cavities (multiple), output cavity, and collector. The electron beam emitted from the electron gun is RF modulated in the input cavity, and bunching progresses in the drift space. RF energy is extracted from the bunched electron beam in the output cavity.

Electronic efficiency is defined as:

$$\eta_{\text{el}} = \frac{P_{\text{RF}}}{V_0 I_0}$$

Values of 50-70% are achieved, where $V_0$ is beam voltage and $I_0$ is beam current.

ITER klystron specifications are: frequency 5 GHz, single-tube output 500 kW, continuous operation 1000 seconds.

Multi-cavity klystrons enable broadband amplification through intermediate cavity tuning. Bandwidth is:

$$\Delta f / f_0 \approx 1-5\%$$

Grill Antennas

Waveguide arrays (grills) are used for lower hybrid wave injection. Many rectangular waveguides are arranged toroidally, and by exciting each waveguide with phase differences, the desired $n_\parallel$ spectrum is generated.

The radiation pattern from a single waveguide is determined by the mode distribution at the aperture. For the TE$_{10}$ mode, the radiated electric field is:

$$E_y(x) = E_0 \cos\left(\frac{\pi x}{a}\right)$$

where $a$ is the waveguide width.

The radiation spectrum from the entire grill is expressed as the product of the single waveguide pattern and the array factor:

$$S(n_\parallel) = |F(n_\parallel)|^2 \cdot |A(n_\parallel)|^2$$

The array factor is:

$$A(n_\parallel) = \sum_{j=1}^{N} \exp\left[i(j-1)\left(\frac{\omega d}{c} n_\parallel - \Delta\phi\right)\right]$$

The $n_\parallel$ peak is controlled by phase difference $\Delta\phi$ and pitch $d$.

Multijunction waveguides are structures aimed at efficient power distribution and miniaturization. Output from one klystron is divided by E-plane junctions (phase reversal) or H-plane junctions (phase preservation) and fed to multiple radiating waveguides.

Phase velocity $v_\phi$ is determined by:

$$v_\phi = \frac{\omega d}{\Delta\phi}$$

Typical designs use $\Delta\phi = 90°$, $d = 10$ mm to generate a peak at $n_\parallel \approx 2$.

For grill antenna thermal design, heat load management on plasma-facing surfaces is a challenge. Waveguide tips are coated with heat-resistant materials (molybdenum, tungsten, etc.).

Current Drive Efficiency

A characteristic of lower hybrid waves is their high current drive efficiency. Current drive efficiency $\eta_{CD}$ is defined as:

$$\eta_{CD} = \frac{n_e I_{CD} R_0}{P_{CD}} \quad [\text{A} \cdot \text{m}^{-2} / \text{W}]$$

Here, $n_e$ is electron density (10$^{20}$ m$^{-3}$), $I_{CD}$ is driven current (A), $R_0$ is major radius (m), and $P_{CD}$ is injected power (W).

The current drive efficiency estimate from Fisch-Boozer theory is:

$$\eta_{CD} \propto \frac{v_\phi^2}{v_\phi^3 + v_c^3}$$

Here, $v_c$ is the collision velocity:

$$v_c = v_{Te} \left(\frac{3\sqrt{\pi}}{4} Z_{\text{eff}} \ln\Lambda \frac{n_e}{n_{17}}\right)^{1/3}$$

Comparing typical current drive efficiencies of each heating method:

Method	$\eta_{CD}$ [10$^{20}$ A/Wm$^2$]	Characteristics
LHCD	0.3-0.5	Highest efficiency, limited to periphery
ECCD	0.15-0.25	Localized, can reach core
NBCD	0.2-0.4	Volume drive, main for non-inductive operation
FWCD	0.1-0.2	Compatible with ion heating

The high efficiency of LHCD is due to efficient interaction between slow phase velocity ($v_\phi/c \approx 0.3-0.5$) waves and electrons.

Characteristics and Challenges

Lower hybrid waves have the advantage of high current drive efficiency but the constraint of difficult penetration to the high-temperature plasma core.

Central penetration difficulties arise from:

1. Accessibility limitation: $n_{\parallel,\text{acc}}$ increases at high density
2. Early Landau damping: Absorption at periphery at high temperature
3. Spectral gap: Mismatch between $n_\parallel$ needed for core access and accessibility

Due to these constraints, LHCD is mainly applied to peripheral current profile control. Specifically:

1. Current profile optimization: Relaxing central peaking to improve MHD stability
2. Current hole operation: Internal transport barrier formation in reversed shear configuration
3. Bootstrap current assist: Non-inductive operation in combination with self-generated current

ITER Heating Systems Overview

ITER combines multiple heating methods to achieve over 73 MW of total heating power.

Heating Method	Power	Primary Use	Efficiency (Wall-Plug)
NBI	33 MW	Main heating, rotation drive, current drive	27%
ECRH	20 MW	Heating, NTM control, startup assist	40%
ICRH	20 MW	Ion heating, minority ion heating	50%
LHCD	Future addition	Current profile control	45%

Wall-plug efficiency $\eta_{WP}$ is defined as the ratio of injected power to power supplied from the electrical grid:

$$\eta_{WP} = \frac{P_{\text{injected}}}{P_{\text{grid}}}$$

Each system is required to operate continuously for 3600 seconds (1 hour), aiming for steady-state operation as a fusion reactor.

Overall system efficiency is determined by the product of efficiencies of each subsystem. Taking NBI as an example:

$$\eta_{WP,\text{NBI}} = \eta_{\text{ion source}} \times \eta_{\text{accel}} \times \eta_{\text{neutral}} \times \eta_{\text{transport}}$$ $$\approx 0.85 \times 0.95 \times 0.58 \times 0.60 \approx 0.27$$

Integration of Current Drive and Heating

In steady-state fusion reactor operation, heating and current drive are closely related challenges. In tokamaks, plasma current forms part of the confinement magnetic field, requiring simultaneous achievement of non-inductive current drive and efficient heating.

Physical Relationship Between Heating and Current Drive

When power injected from external sources is absorbed by the plasma, heating and current drive may compete. The relationship between heating efficiency $\eta_h$ and current drive efficiency $\eta_{CD}$ depends on the spectrum and injection angle of the injected wave.

Current drive is achieved by creating asymmetry in the velocity distribution of electrons or ions. Generally, current drive efficiency is defined as:

$$\eta_{CD} = \frac{I_{CD} R_0 n_e}{P_{CD}} \quad [10^{20} \text{ A/W m}^2]$$

Here, $I_{CD}$ is driven current, $R_0$ is major radius, $n_e$ is electron density, and $P_{CD}$ is input power. This definition is normalized to scale with device size and density.

The relationship between current drive power density and heating power density depends on absorption process details. Generally:

$$\frac{P_{CD}}{P_{abs}} + \frac{P_{h}}{P_{abs}} = 1$$

By optimizing injection conditions, the balance between the two is controlled.

Current Drive by NBI (NBCD)

In NBI, when injected fast ions slow down in the plasma, net current is driven through collisions with electrons. By tilting the injection angle, the parallel momentum component of fast ions is controlled to optimize current drive efficiency.

NBCD current drive efficiency is approximated by:

$$\eta_{NBCD} \approx \frac{T_e}{20} \cdot \frac{1}{1 + Z_{\text{eff}}/5} \cdot F(E_b/E_c) \quad [10^{20} \text{ A/W m}^2]$$

Here, $T_e$ is electron temperature in keV, $Z_{\text{eff}}$ is effective charge, $E_b$ is beam energy, and $E_c$ is critical energy. Function $F$ depends on $E_b/E_c$, with optimal values at $E_b \approx 2-3 E_c$.

Characteristics of NBCD include:

1. Volume current drive: Current is driven throughout the beam slowing-down region
2. Simultaneous toroidal rotation drive: Contributes to plasma stabilization
3. Fast ion distribution control: Adjustable by injection angle and energy

$$I_{NBCD} = \int j_{NBCD}(r) \, 2\pi r \, dr$$

The current distribution $j_{NBCD}(r)$ is obtained by fast ion orbit-following calculations.

ECCD (Electron Cyclotron Current Drive)

By injecting ECRH obliquely, electron cyclotron current drive (ECCD) is possible. Through the Fisch-Boozer mechanism, the velocity distribution of resonant electrons is asymmetrized, generating net current.

The theoretical efficiency of ECCD is:

$$\eta_{ECCD} = \frac{0.041}{(1 + \theta^{1.5}) Z_{\text{eff}}} \cdot T_e \cdot \xi$$

Here, $\theta = T_e / 5.11 \times 10^3$ keV is the relativistic parameter, and $\xi$ is a geometric factor depending on injection angle.

The greatest advantage of ECCD is its locality. Since absorption location can be precisely controlled:

$$\delta j_{ECCD}(r) = \frac{P_{ECCD}}{2\pi R_0} \cdot \frac{\eta_{ECCD} n_e}{r \Delta r}$$

localized current density perturbations can be applied. This enables driving current directly inside neoclassical tearing mode (NTM) magnetic islands to stabilize the modes.

The NTM stabilization condition is expressed by the relationship between island width $w$ and driven current:

$$\frac{\partial w}{\partial t} \propto -\Delta' w - \frac{j_{BS}}{j_{ECCD}} + \frac{w_{sat}^2}{w}$$

Here, $\Delta'$ is the tearing mode stability parameter and $j_{BS}$ is the bootstrap current density. If $j_{ECCD}$ compensates for $j_{BS}$, the mode is stabilized.

FWCD (Fast Wave Current Drive)

This method excites traveling waves from ICRH antennas and drives current through electron Landau damping or TTMP (Transit Time Magnetic Pumping).

By controlling the $n_\parallel$ spectrum of fast waves, the sign and magnitude of driven current are adjusted:

$$k_\parallel = \frac{\Delta\phi}{d} + \frac{n}{R_0}$$

Here, $\Delta\phi$ is the inter-strap phase difference, $d$ is strap spacing, and $n$ is the toroidal mode number.

FWCD efficiency is lower than LHCD or ECCD, but has the advantage of simultaneously driving current and heating ions:

$$\eta_{FWCD} \approx 0.1 - 0.15 \quad [10^{20} \text{ A/W m}^2]$$

Optimization of Current Profile Control

By combining various current drive methods, the target current profile $j(r)$ is achieved. The optimization problem is formulated as:

$$\min \sum_i P_i \quad \text{s.t.} \quad \sum_i j_i(r) + j_{BS}(r) = j_{target}(r)$$

Here, $P_i$ is the input power of each method, $j_i(r)$ is the current density from each method, and $j_{BS}(r)$ is the bootstrap current density.

Control of the safety factor $q$ profile directly affects MHD stability and confinement performance:

$$q(r) = \frac{r B_\phi}{R_0 B_\theta} = \frac{2\pi r^2 B_\phi}{\mu_0 R_0 I_p(r)}$$

Negative or weak positive magnetic shear $s = r q'/q < 0$ is effective for internal transport barrier (ITB) formation, achieved by combining LHCD and ECCD.

Integrated Comparison of Methods

Comparison of Energy Deposition Targets

Each heating method has different characteristics depending on whether energy is deposited to electrons or ions:

$$\frac{dW_e}{dt} = P_{e,abs} - P_{ei} - P_{e,loss}$$ $$\frac{dW_i}{dt} = P_{i,abs} + P_{ei} - P_{i,loss}$$

Here, $P_{ei}$ is the electron-ion energy exchange term:

$$P_{ei} = \frac{3 n_e (T_e - T_i)}{\tau_{ei}}$$

The equipartition time $\tau_{ei}$ is:

$$\tau_{ei} = \frac{3 m_e m_i}{8 \sqrt{2\pi} n_e Z^2 e^4 \ln\Lambda} \left(\frac{T_e}{m_e} + \frac{T_i}{m_i}\right)^{3/2}$$

At high temperatures, $\tau_{ei}$ becomes long, and the distinction between electron and ion heating becomes clear.

Heating Method	Primary Target	Effect on $T_e/T_i$	Notes
NBI (positive ion)	Ion dominant	Tendency for $T_i > T_e$	Lower energy favors ion heating
NBI (negative ion/high energy)	Electron dominant	Tendency for $T_e > T_i$	Above critical energy
ECRH	Electrons only	$T_e \gg T_i$ possible	No direct ion heating
ICRH (minority ion)	Ion dominant	Tendency for $T_i > T_e$	Heats minority ion species
ICRH (2nd harmonic)	Ions	$T_i \approx T_e$	Direct heating of main ion species
LHCD	Electrons only	Tendency for $T_e > T_i$	Via Landau damping

In D-T fusion, ion temperature determines the reaction rate, so maintaining high $T_i$ is important. However, electron temperature also affects confinement performance, requiring a balance between the two.

Heating Location and Penetration Depth

The heating location of each method is determined by injection conditions and plasma parameters.

NBI penetration depth is characterized by attenuation length $\lambda$:

$$\lambda = \frac{v_b}{\langle\sigma v\rangle_{ion} n_e + \langle\sigma v\rangle_{cx} n_0}$$

Here, $v_b$ is beam velocity, and $\langle\sigma v\rangle_{ion}$ and $\langle\sigma v\rangle_{cx}$ are reaction rate coefficients for ionization and charge exchange respectively. Higher energy beams have greater penetration depth and can reach the plasma core:

$$\frac{I(x)}{I_0} = \exp\left(-\int_0^x \frac{dx'}{\lambda(x')}\right)$$

RF heating absorption location is determined by resonance conditions.

ECRH resonance location is determined by magnetic field strength:

$$R_{res} = R_0 \frac{B_0}{B_{res}} = R_0 \frac{n \omega_{ce,0}}{\omega}$$

Here, $n$ is the harmonic number. By adjusting injection location and angle, $R_{res}$ is controlled.

ICRH resonance layer is also determined by magnetic field strength, but may encounter cutoffs during propagation from the plasma periphery:

$$\omega_{cf}^2 = \omega_{ci}^2 + \omega_{pi}^2$$

Unless the frequency exceeds the cutoff frequency $\omega_{cf}$, the plasma core cannot be reached.

LHCD penetration depth is limited by the accessibility condition:

$$n_{\parallel,acc} = 1 + \frac{\omega_{pe}}{\omega_{ce}}$$

At high-density regions, $n_{\parallel,acc}$ increases and waves are reflected, making core access difficult.

Comprehensive Efficiency Comparison

The efficiency of each heating method is evaluated by accumulating losses at multiple stages:

$$\eta_{total} = \eta_{source} \times \eta_{transmission} \times \eta_{coupling} \times \eta_{absorption}$$

Method	Source Efficiency	Transmission Efficiency	Coupling Efficiency	Absorption Efficiency	Total Efficiency
NBI	85%	95%	60%	95%	27%
ECRH	50%	85%	95%	99%	40%
ICRH	65%	90%	85%	95%	47%
LHCD	55%	85%	80%	95%	35%

Here, source efficiency is the power efficiency of sources (ion source, gyrotron, etc.), transmission efficiency is transmission system losses, coupling efficiency is coupling to plasma (including neutralization for NBI), and absorption efficiency is absorption rate in plasma.

For current drive-focused comparison, the following metric is useful.

Power consumption per driven current:

$$\gamma = \frac{P_{grid}}{I_{CD}} = \frac{n_e R_0}{\eta_{CD} \eta_{WP}} \quad [\text{W/A}]$$

For ITER parameters ($n_e = 10^{20}$ m$^{-3}$, $R_0 = 6.2$ m):

Method	$\eta_{CD}$	$\eta_{WP}$	$\gamma$ [MW/MA]
NBCD	0.30	0.27	77
ECCD	0.20	0.40	78
LHCD	0.40	0.35	44
FWCD	0.15	0.47	88

This shows LHCD has the highest power efficiency. However, due to penetration depth constraints, combinations of multiple methods are necessary in actual operation.

Application Range of Each Method

Each heating method has an application range where it functions most effectively:

Application	Recommended Method	Reason
Plasma startup	ECRH	Injection possible at low density without cutoff
Main heating (bulk heating)	NBI, ICRH	High power, ion heating capability
Core heating	NBI, ECRH	High penetration capability
Current profile control	LHCD, ECCD	High current drive efficiency, locality
NTM control	ECCD	Precise localized current drive
Rotation drive	NBI	Momentum injection
Fast ion generation	NBI, ICRH	Simulation of alpha particle physics

Future reactors will be designed with optimal combinations of heating systems considering these characteristics.

Heating and Current Drive in Future Reactors

For future reactors beyond DEMO (demonstration reactor), requirements for heating systems become even more stringent.

Importance of Current Drive

Non-inductive current drive is essential for steady-state tokamak reactor operation. The required driven current $I_{CD}$ has a complementary relationship with bootstrap current $I_{BS}$:

$$I_p = I_{BS} + I_{CD}$$

The bootstrap current fraction $f_{BS}$ is:

$$f_{BS} = \frac{I_{BS}}{I_p} \propto \beta_p \epsilon^{1/2}$$

Here, $\beta_p$ is poloidal beta and $\epsilon = a/R_0$ is inverse aspect ratio.

DEMO targets $f_{BS} \approx 0.5-0.7$, with the remainder supplied by external current drive. The required current drive power is estimated as:

$$P_{CD} = \frac{(1 - f_{BS}) I_p R_0 n_e}{\eta_{CD}}$$

Technology Development for Efficiency Improvement

Efficiency improvements for each system are being advanced for application to future reactors.

For NBI systems, the goal is to improve neutralization efficiency from 60% to 95% through practical photoneutralization. This would improve wall-plug efficiency to over 40%:

$$\eta_{WP,\text{future}} = 0.85 \times 0.95 \times 0.95 \times 0.60 \approx 0.46$$

For ECRH systems, the goals are development of 2 MW-class gyrotrons and achieving over 60% efficiency through multi-stage energy recovery.

For ICRH systems, RF sheath reduction technology (such as field-aligned antennas) will suppress impurity release while enabling high power density operation.

Compatibility with Tritium Breeding Ratio

Future reactors must maintain a tritium breeding ratio (TBR) above 1 to close the fuel cycle. Heating ports penetrate the breeding blanket and negatively affect TBR:

$$\Delta \text{TBR} \propto \frac{A_{\text{port}}}{A_{\text{FW}}}$$

Here, $A_{\text{port}}$ is port opening area and $A_{\text{FW}}$ is total first wall area. NBI ports require particularly large openings, raising concerns about TBR impact.

Countermeasures being considered include: injection port diameter reduction (beam optics optimization), power requirement reduction through efficiency improvement, and bootstrap current fraction enhancement.

Equipment Reliability Under Neutron Irradiation

In the fusion reactor environment, material damage from 14 MeV neutrons is a concern. Damage from neutron fluence $\Phi$ is evaluated as:

$$\text{dpa} = \sigma_d \Phi$$

Here, $\sigma_d$ is the damage cross-section.

Plasma-facing components of heating systems (antennas, port shielding, etc.) require material selection resistant to irradiation damage and maintainability for replacement.

For ECRH launcher mirrors, degradation of optical properties under neutron irradiation is a concern. Molybdenum mirror reflectivity decreases as:

$$R(\Phi) = R_0 \exp(-\alpha \Phi)$$

requiring periodic replacement.

ICRH antenna Faraday shields are exposed to combined neutron irradiation and ion bombardment environments. Transition to low-activation materials such as tungsten alloys or beryllium is being considered.

Design Guidelines for Future Reactor Heating Systems

For heating system design beyond DEMO, the following guidelines are important:

1. Wall-plug efficiency over 40%: Minimization of recirculating power
2. Minimization of blanket penetration area: Ensuring TBR > 1.1
3. Continuous operation over 1 year: High reliability and maintainability
4. Remote maintenance capability: Equipment replacement in high-radiation environment

Integrated optimization of heating systems is being advanced to meet these requirements.

Future Challenges

The main development challenges for each heating system are summarized below.

NBI challenges:

1. Injection port diameter reduction (ensuring tritium breeding ratio)
2. Practical photoneutralization for efficiency improvement
3. Long-term stable operation of negative ion sources (Cs management technology)
4. Equipment reliability enabling over 1-year continuous operation

ECRH challenges:

1. High-frequency, high-power gyrotron development (over 2 MW)
2. Further improvement of energy recovery efficiency
3. Mirror durability under neutron irradiation
4. Advanced MHD control through real-time scanning

ICRH challenges:

1. Suppression of impurity release by RF sheaths
2. Antenna area reduction (TBR assurance)
3. High power density operation
4. Stabilization of plasma coupling

LHCD challenges:

1. Wave propagation technology to high-temperature plasma core
2. Solution to spectral gap problem
3. Grill antenna thermal design optimization
4. Specialization in peripheral current control and role sharing with other methods

Solving these challenges will enable efficient heating and current drive systems for future fusion power plants.

Related Topics

• Principles of Plasma Heating - Fundamentals of heating physics
• Superconducting Coils - Magnetic field generation systems
• ITER Project - World’s largest tokamak experimental reactor
• Tokamak Configuration - Overview of confinement approach
• MHD Instabilities - Control targets for ECRH