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Nature Physics 12, 14–17 (2016) doi:10.1038/nphys3625
Published online 07 January 2016
Didier Mazon, Christel Fenzi & Roland Sabot
Sustaining and measuring high temperatures in fusion plasmas is a challenging task that requires different heating systems and diagnostic tools. Information on the spatial distribution of temperature is one of the key elements for improving and controlling plasma performance.
At a glance
A current pulse in the inner poloidal field coils (primary transformer winding), located in the hole of the torus, creates an electric field that drives a large current Ip (of the order of a few MA) in the plasma ring, which serves as the sole winding of a secondary transformer. This plasma current induces a poloidal magnetic field component acting on the plasma. In conjunction with the toroidal magnetic field generated by coils placed around the torus, this causes each field line to spiral around the plasma torus, defining a surface of constant magnetic flux. Particles orbiting a field line are constrained near this surface, unless they collide with other particles. To control the radial drift of plasma particles, a vertical magnetic field is applied by means of outer poloidal field coils to produce a radially inward force on the plasma ring.
Ohmic heating is generated by driving a large current through the plasma itself. Highly kinetic extra fuel particles, injected into the tokamak, transfer energy through collisions with the plasma particles (neutral beam injection heating). Injected electromagnetic waves, with carefully chosen frequencies, are damped and pass on energy to the plasma (radio-frequency heating). Once fusion reactions have started, kinetic alpha-particles (4He2+ ions, α) are produced (together with neutrons, n) that, by colliding, transfer their kinetic energy to other plasma particles, keeping the plasma hot. Adapted with permission from ref. 20, Veen Media.
Profiles of Ti are inferred from combined XICS and CXRS measurements, and additional information on Ti at the centre is provided by neutron rate analysis (the width of the neutron spectrum is proportional to Ti1/2). Profiles of Te are inferred from XICS, Thomson scattering and ECE methods. The data were recorded during a high-density H-mode (high-confinement) plasma in the Alcator C-Mod tokamak. The major plasma radius (R) is the distance from the torus axis in the equatorial plane, as shown in the illustration of the tokamak geometry. The magnetic axis (here at R ≈ 0.69 m) refers to the plasma centre position (that is, the centre of the last closed magnetic flux surface). Figure adapted from ref. 6, AIP.
In the Sun — and other stars — energy is produced as a by-product of fusion reactions converting hydrogen into helium. A figure of merit for this process is the 'reactivity', which is the product of the reaction probability and the energy delivered per reaction. The overall reaction probability of fusion in the Sun is extremely low, but nevertheless sufficient to generate an energy stream of around 1024 kW because the particles participating in the Sun's fusion processes are held together strongly enough by gravity for reactions to occur. In the core of the Sun, the temperature is 10–15 million °C. Together with the extreme pressure (a quarter of a trillion atmospheres) and densities (around 5 × 1031 electrons per m3 and a mass density of around 160 g per cm3 — eight times that of gold), this allows matter to be converted into large amounts of energy.
Fusion on Earth
The idea of realizing fusion on Earth as a source of energy has been around since the 1920s1. To do so, it is necessary to heat a gas of hydrogen isotopes to a temperature ten times higher than that in the Sun's core. (Higher temperatures are required because the particle density in the Sun's core simply cannot be achieved on Earth; the best one can manage is around 1020 m−3.) At such temperatures, hydrogen atoms (isotopes) become fully ionized: protons, neutrons and electrons form a plasma, sometimes called the fourth state of matter. The fusion reaction between a deuterium (2H or D) and a tritium (3H or T) atom has maximum reactivity at around 100 million °C, and produces a 4He atom and a neutron, both with a certain amount of kinetic energy: D + T 
n (14 MeV) + 4He (3.5 MeV). One approach for confining the hot plasma, which would otherwise disintegrate owing to repulsive Coulomb forces, uses the interaction between charged particles and a magnetic field. A charged particle is deflected by a magnetic field and, if the field is strong enough, the particle will orbit around a magnetic field line, gradually progressing along the line if it has a longitudinal velocity component. This notion lies at the basis of magnetic-confinement fusion, which has been researched since the 1950s2.
Shortly after the Second World War, the tokamak — a Russian acronym for toroidal chamber with magnetic coils — was devised by Soviet scientists as a solution for confining and sustaining a hydrogen plasma (the deuterium–tritium fuel mixture). Although the plasma is neutral overall, it can carry an electrical current through the independent propagation of positively and negatively charged particles of which it is composed. In a tokamak (Fig. 1), a plasma is kept in a toroidally shaped chamber, with confinement provided by a clever configuration of coils (producing magnetic fields) and transformer circuits, taking advantage of the plasma's intrinsic capability of carrying a large current.
Figure 1: Schematic of a tokamak.
© EUROFUSION
Heating the plasma
To initiate the fusion reaction, air and impurities are removed from the inside of the tokamak — essentially a toroidal vacuum chamber. The magnetic coils that confine the plasma are turned on, and low-density gaseous fuel is introduced into the vacuum vessel by means of a gas injection system. An electric current is then applied, which causes the gas to break down electrically (ionize) and form a plasma.
The first source of heat in the plasma is the electric current running through it, inducing ohmic (resistive) heating. Plasma resistance heating gets increasingly weaker with increasing plasma temperature, however, and at about 10 million °C, resistive heating alone cannot overcome power losses from heat radiation.
Alpha-particle heating is produced when the (positively charged) 4He nuclei resulting from the fusion reactions are trapped by the magnetic field and slowed down when colliding with plasma electrons. This is the mechanism that is crucial for sustaining a burning plasma. But at 10 million °C there are still insufficient alpha-particle reactions to heat up the plasma; about 100 million °C is needed for them to become significant. Bridging the gap requires external heating schemes.
One approach is heating by neutral beam injection: fuel deuterium ions are accelerated, made to collide with deuterium gas or a neutralizer, which neutralizes them, then allowed to cross the tokamak's confining magnetic field, after which they are ionized by the plasma and trapped by the magnetic field. They subsequently transfer their energy to the plasma through collisions.
Another method is radio-frequency heating, the injection of electromagnetic waves into the plasma. Usually, most of the plasma particles are a little slower than the wave; hence, electromagnetic waves will experience drag and be damped by the plasma. Such collisionless (or Landau) damping transfers energy between the waves and the plasma particles. The energy is delivered to the plasma by antennas or waveguides at the plasma's edge. The frequencies are tuned so that the energy is absorbed in the appropriate region of the plasma and by the appropriate particles — electrons and ions do not gyrate at the same frequency and are not affected in the same way by the wave. The different heating schemes are visualized in Fig. 2.
Figure 2: Different sources of heating in a tokamak.
Measuring the plasma temperature
Measuring plasma parameters, such as temperature, density, current and impurity content, poses great challenges because any probe would be destroyed inside the plasma. Several indirect measurement techniques have been developed, and nowadays tokamaks are usually equipped with more than 50 pieces of diagnostic equipment3. For the main parameters such as density and temperature, multiple measurements based on different techniques are the norm for validating and cross-checking data. Plasma core characteristics are mostly probed by means of the light (from microwaves to X-rays) emitted from the plasma.
To analyse heat and particle transport within the plasma, spatially and temporally resolved measurements of temperature profiles are needed to monitor the plasma response to external heating. Temperature gradients also play an important role in plasma turbulence leading to loss of confinement, and precise knowledge of such gradients is necessary for detailed comparisons with theoretical predictions from modern computer codes.
Importantly, the ion and electron plasma temperatures may not be equal. In a dense plasma, collisions tend to attenuate the difference between electron and ion temperature. At the edge, or in the case of predominant heating of a specific species, this attenuation is weaker. Ion and electron temperatures can be decorrelated, with a ratio as high as 2. Measuring the temperature profile of both types of particles is thus mandatory for evaluating the plasma's response to additional heating or computing the energy transport coefficient.
Measuring ion temperature
Two complementary techniques, based on 'active beam' and 'passive emission' spectroscopy, can be used for measuring the plasma ion temperature Ti; information on Ti can also be inferred from neutron spectroscopy4. Both methods provide measurements of Ti from the Doppler broadening Δλ of plasma ion emission spectral lines (assuming a Maxwellian distribution for ion velocities) through the relationship Ti = (mc2/2kB)(Δλ/λ0), where m is the ion mass, c is the speed of light, kB is the Boltzmann constant, Δλ is the spectral line width and λ0 is the rest wavelength.
Charge-exchange recombination spectroscopy (CXRS)5 is an 'active spectroscopy' technique in the sense that it relies on the use of an external beam of energetic neutral particles (H2 or D2) injected into the plasma. The method enables highly localized measurements (along the beam path) from the visible spectral emission of fully electron-stripped plasma ions (light impurity ions such as C6+ or He2+, providing intense line emissions) that undergo charge-exchange reactions with the neutral beam particles. This technique, however, causes a perturbation in the plasma. Moreover, as the beam penetrates into the plasma, it is attenuated by the increasingly dense plasma so that measurement accuracy can be affected.
In contrast to CXRS, high-resolution X-ray imaging crystal spectroscopy (XICS) is a 'passive spectroscopy' technique as it simply relies on the spectral analysis of plasma radiative losses (due to intrinsic ion emission lines arising from the interactions between the plasma and the wall material, or due to externally injected impurity ion emission lines), and specifically the emission from highly charged impurity ions (such as Fe24+, Ar17+ or Ar18+) in the soft X-ray range (up to 15 keV)6. In this range, standard diffraction gratings cannot be used, and crystals (typically quartz or germanium) are used instead for spectral diffraction. The XICS technique makes use of the astigmatism properties of spherically bent crystals7 arranged on a spectrometer in Johann-type configuration8, with a high-count-rate two-dimensional detector9. The double Bragg reflections of the light emitted by the plasma on the surface of the crystals provide both spatial and spectral resolutions. Radial Ti profiles with ~1 cm spatial resolution and time resolution <10 ms are typically obtained, with 1% statistical uncertainty, allowing the precise determination of temperature gradients and studies of fast physical phenomena. It is also worth mentioning that information on the electron temperature Te can be obtained with this technique, by using intensity ratios of carefully chosen pairs of lines from the measured spectrum — under certain conditions, these ratios depend on Te only.
Figure 3 shows typical measurements of tokamak plasma temperature profiles, presenting results obtained for Ti and Te with different measurement methods.
Figure 3: Temperature profile measurements obtained with different methods.
Profiles of Ti are inferred from combined XICS and CXRS measurements, and additional information on Ti at the centre is provided by neutron rate analysis (the width of the neutron spectrum is proportional to Ti1/2). Profiles of Te are inferred from XICS, Thomson scattering and ECE methods. The data were recorded during a high-density H-mode (high-confinement) plasma in the Alcator C-Mod tokamak. The major plasma radius (R) is the distance from the torus axis in the equatorial plane, as shown in the illustration of the tokamak geometry. The magnetic axis (here at R ≈ 0.69 m) refers to the plasma centre position (that is, the centre of the last closed magnetic flux surface). Figure adapted from ref. 6, AIP.
Measuring electron temperature
Several techniques have been developed for measuring the electron temperature in a fusion apparatus10. At the very edge of the plasma, where the density is low and the temperature is only 104–105 K, fixed probes known as Langmuir probes — essentially consisting of one or more electrodes — provide a local measurement of the temperature.
For the plasma core, two techniques are mainly used. Thomson scattering relies on the scattering of an intense laser beam by the plasma electrons. The scattered beam intensity is proportional to the local electron density, and its spectral width is linked to the local temperature11. The time resolution is set by the laser repetition rate (typically of the order of tens of milliseconds), while the spatial resolution (which can be as low as a few millimetres) improves with the beam intensity. Diagnostics with high-intensity laser banks have been developed to follow fast events12. At the end of the 1960s, validation by a British team with a Thomson scattering diagnostic of a temperature above 100 million °C in the Soviet T3 tokamak11 marked the rise of tokamaks as the most successful fusion configuration.
Microwave radiometry is the other main technique for electron temperature measurement. It has similarities to radiometers developed for measuring the temperature of cosmic objects such as gas clouds or planetary emission. In a magnetically confined plasma, charged particles gyrate around the magnetic field lines and, as a consequence, emit electromagnetic radiation at the cyclotron frequency and its harmonics — electron cyclotron emission (ECE)10. For electrons, the cyclotron frequency f is 28 GHz for a magnetic field of 1 T. The core of a magnetic fusion device is optically thick for the first and second harmonics of ECE radiation. A local thermodynamic equilibrium is then reached, and the ECE intensity approaches the black-body level. The ECE frequency range, 50–150 GHz, corresponds in radioastronomy to the cosmic microwave background of black-body radiation at only ~3 K, seven orders of magnitude colder than the core of a fusion plasma. The low-frequency limit (Rayleigh–Jeans law) applies to ECE emission, and the intensity profile I(R) is proportional to the local electron temperature Te: I(R) = f2Te(R)/2π2c2, with R the major plasma radius (the position in the plasma relative to the torus axis in the equatorial plane).
In a tokamak, the magnetic field varies in toroidal geometry monotonically as 1/R along the major plasma radius, resulting in an ECE spectrum that is a broad continuum. To reconstruct the electron temperature profiles, one has to measure, with a band-filtering heterodyne radiometer, the emission intensity along the line of sight in several frequency bands. The frequency of each channel determines the radial position, and the intensity gives the local electron temperature13.
As the ECE instantaneous signal is extremely noisy, sensitivity and time resolution are entangled. Precise temperature profiles (<1%) can be provided at millisecond rates, but ECE can also detect large temperature fluctuations (a few per cent) induced by high-frequency (>10 kHz) instabilities. Correlating two ECE channels reduces thermal noise and allows the retrieval of temperature fluctuations induced by plasma turbulence.
More recently, ECE imaging diagnostics have been developed14. The single antenna of a classic one-dimensional ECE is replaced by an array of antennas equivalent to several radiometers stacked vertically. By using large-diameter optics and refocusing elements, the beam waist can be decreased to 1–2 cm and the radial resolution can reach 0.5–1 cm.
Controlling temperature gradients
Turbulence tends to decrease plasma heat and particle confinement, and thus also decreases reactivity. Plasma regimes showing an 'internal transport barrier' (ITB)15, a region in the central part of the plasma where turbulent transport is locally reduced, have an increased plasma reactivity. Practically, an ITB is characterized by large pressure gradients and by the presence of a visible break in the slope of the electron and ion temperature profiles16. A way to optimize the plasma performance is thus to control temperature gradients.
A simple criterion characterizing the emergence and spacetime evolution of ITBs has been proposed17, involving the dimensionless parameter ρT* = ρs/LT — the ratio of the local ion Larmor radius at the speed of sound, ρs, and the scale length of the electron- or ion-temperature gradient LTe or LTi. An ITB exists when the normalized Larmor radius ρT* exceeds a critical value. A dimensional analysis allows one to interpret this criterion of ITB existence from the point of view of microturbulence. It seems to be associated with the stabilization of some turbulent modes through the combined effect of the electric and magnetic fields that are able to decorrelate turbulent zones in the plasma18. This practical ITB criterion is now being routinely used to speed up the identification of the time and location at which an ITB appears. Ultimately, it might be used to control the ITB dynamics19, and thus potentially the plasma performance, in real time.
References
- Physics World 47–51 (October 2010).
- Nucl. Fusion 12, 215–252 (1972).
- Fusion Sci. Technol. 56, 1219–1252 (2009).
- Nucl. Fusion 47, S337–S384 (2007).
- et al. Rev. Sci. Instrum. 61, 3479–3486 (1990).
- et al. Rev. Sci. Instrum. 79, 10E302 (2008).
- , , , & Rev. Sci. Instrum. 66, 530–532 (1995).
- , & J. Phys. B 29, 3787–3797 (1996).
- et al. Nucl. Instrum. Methods Phys. Res. A 501, 260–266 (2003).
- Principles of Plasma Diagnostics (Cambridge Univ. Press, 2002).
- , , , & Nature 224, 488–190 (1969).
- et al. Plasma Phys. Control. Fusion 52, 124041 (2010).
- et al. Rev. Sci. Instrum. 76, 123501 (2005).
- et al. Rev. Sci. Instrum. 74, 4239–4262 (2003).
- et al. Nucl. Fusion 44, R1–R49 (2004).
- et al. Plasma Phys. Control. Fusion 40, A251–A268 (1998).
- et al. Nucl. Fusion 42, 520–526 (2002).
- , & Phys. Plasmas 1, 2229–2244 (2004).
- et al. Plasma Phys. Control. Fusion 44, 1087–1104 (2002).
- & Natuur Techniek 63, 2–17 (1995).