The first document on the energy source of the stars and sun [1] opened a century-long dream of fusion energy. The theory of quantum tunneling to overcome the Coulomb barrier was critical for the possibility of laboratory fusion energy development. Through long research on developing fusion plasmas, an apex of fusion plasma research was reached with three large tokamak eras (TFTR, JET, and JT-60U). The discovery of improved confinement regimes and relevant scaling laws supported by confinement physics models were the basis of the current ITER project and other DEMO programs throughout the world.

This paper critically reviews the causality of improved energy confinement regimes in toroidal magnetic devices, energy confinement scaling laws, and performance data. Following the discovery of high confinement mode (H-mode) in tokamak plasmas, when a diverted magnetic configuration with an x-point between the last closed flux surface (LCFS) and divertor plate surface was introduced in ASDEX, Germany [2], shaped plasma with divertor configurations has dominated over circular plasmas with limiters. In H-mode plasmas, the improved confinement region has been dominantly at the edge region compared to that of the L-mode plasmas, and it has been labeled as an edge transport barrier (ETB). Initially, H-mode pedestal pressure was pronounced by edge T_e and slowly evolved to n_e dominant pedestal. There are reports on improved confinement between L-mode and H-mode such as QH-mode and I-mode and edge pedestal of divertor system at lower field side (negative triangularity). The research effort on formation of ETB has been mostly focused on suppression mechanisms of the various gradient driven turbulences through E_rxB effect.

A new model for edge confinement based on the interplay between inflow and outflow plasmas across the LCFS is suggested in this paper. Here, the “inflow plasmas” are defined as the plasmas transported across the LCFS originating from divertor surfaces (i.e., high recycling rate), and “outflow plasmas” are the plasmas transported across LCFS to the surfaces of divertor. A new potential source of E_r inside the LCFS is suggested, possibly due to ∇B drift in the vicinity of the x-point, and this is compared with conventional turbulence suppression mechanisms via E_rxB effects through measured edge turbulences. The source of high turbulence observed at the edge of the L-mode plasmas in both limiter and diverted plasmas can be from the inflow plasmas, and the turbulence part can induce enhanced particle transport which enhances the outflow plasma which can provoke more inflow plasmas until the surface of limiter and divertor is well conditioned.

In this new model, another quantity useful for edge confinement of the closed magnetic confinement system is the “flow impedance” which represents impedance of the plasma flow between LCFS and the surfaces of divertor plates. This concept is employed to explain the variation of edge confinement of toroidal devices and can be applied in the design of a divertor system for an optimum flow impedance that can effectively control the inflow plasmas and the required heat dissipation. Examples are “super-x” and “snowflake” that have a long leg of x-point between LCFS and divertor plates; however, smarter design may be needed for compact device. As the heating power level increased, improved confinement was observed in the core region, and this regime was labeled as an internal transport barrier (ITB). The ITB is based on a steep pressure gradient formed near the core region of the plasma, and formation of ITB in the core has been observed in both edge magnetic configurations with limiter and divertor. The improved confinement inside the ITB has been attributed to the turbulence suppression mechanisms like h_i marginality and the breaking of streamers via E_rxB effect or q-profile shear [3]. But there is no coherent model that supports ITB formation other than that ITB formation cannot be obtained without effective core heating.

An auxiliary heating system is essential to achieve high ion temperature (T_i > 10 keV) essential for ignition regime where sufficient α-particle power can sustain ignition state in fusion devices. The heating method is divided into two categories: electron heating and ion heating. Direct ion heating by positive neutral beam (PNB) has been effective, but application to a large device and/or high-density plasmas is challenging. On the other hand, application of electron heating in high density and/or large devices can be effective, but there are unresolved issues such as central density pump-out, early saturation of ion temperature, and no high-power experimental data (> 10 MW). Notably, ITER plans to include ~80 MW of electron cyclotron resonance heating (ECRH) system.

The confinement time scaling and performance data accumulated for half a century are examined to project a logical path for the most probable compact ignition test device in magnetic fusion. For practical fusion energy production, it is imperative to build experience with an ignition test device that can produce sufficient fusion power prior to electricity generation. These experiences include comprehensive actuators for control of performance and stability, fusion material test, and power conversion system. A tokamak device with plasma volume of ~240 m³ with PNB power < 40 MW is a probable candidate. The goal of this test device is fusion power output of ~220 MW at a moderately high density. With this level of fusion power, α-particle power up to ~60 MW may be sufficient to test the ignition state as well as transition physics from external (PNB) to internal α-heating.

The first document on fusion possibility was published in 1929 by Atkins and Houterman [1], suggesting that the energy source of stars might be from fusion reactions. Eventually, the fusion reaction was demonstrated by Oliphant, and Sir Rutherford proposed the “Moonshine” project for fusion energy development based on beam-target experiment [4]. A theoretical breakthrough came from G. Gamow who suggested a feasibility of practical fusion reaction at ~10-keV ion temperature through quantum tunneling to overcome the Coulomb barrier in 1935. H. Bethe established the fusion energy cycle of the sun, which explains the ~5 billion years lifetime of the sun in 1939, and he received the Nobel Prize in 1967. Among various fusion reactions, the most practical fusion reaction in the laboratory is deuterium-tritium (DT) reaction which has sufficient cross section at ~10–20-keV ion temperature, while the next approachable reaction of deuterium-He₃ reaction requires ~100 keV. A self-sustainable fuel for DT reaction is feasible through lithium which can produce tritium with abundant deuterium from ocean water. However, self-sustained tritium production has yet to be demonstrated due to lack of adequate neutron source.

Many laboratory experiments have been conducted using various magnetic confinement concepts, and they are divided into two categories: open and closed magnetic configurations. Examples of open systems include pinch devices and magnetic mirrors; closed systems include spheromak, field-reversed configuration (FRC), stellarator, and tokamak. In general, the closed system performed better than the open system which has intrinsic loss mechanisms. The early experiments of closed system were hampered by numerous instabilities, and the first promising confined plasma was demonstrated in T3 tokamak, the former Soviet Union. Here, the electron temperature was measured to be ~1 keV by British scientists in 1958. Since then, many stellarators and tokamaks have been challenged by Japan, Europe, Russia, and the USA. Early research devices were based on water-cooled Cu magnet, and the discharge was based on a short pulse due to limitation of cooling. The representative experimental devices were TFTR, USA; JT-60U, Japan; and JET, EU. TFTR and JET are only fusion devices which performed DT experiment, and JT-60U projected fusion power based on DD experiment. These three devices achieved roughly Q~1 (scientific breakeven) at ~40-MW heating power. However, the ignition state of magnetic fusion has never been demonstrated.

After successful demonstration of near “scientific breakeven” condition, steady-state capable devices with superconducting magnets have been developed to support steady-state plasmas (ignited plasma operation) for the future. Examples are LHD, Japan, and W7-X, Germany, for stellarator concept, and KSTAR, Korea, EAST, China, and SST, India, are for tokamak concept. The first international effort to achieve the goal of fusion energy development was briefly initiated in 1978 under the name of “INTOR,” and then it took a long time to be transformed into the ITER program in 1987. The proposed original ITER program was incredibly large device (i.e., V_P > 2000 m³) based on L-mode confinement scaling law. Discovery of high confinement mode (H-mode) in a diverted plasma in ASDEX, Germany, opened a possibility of a smaller size ITER (V_P ~900 m³). It took more than ~20 years to materialize a practical international fusion program, and construction of ITER is in progress at Saint Paul-les-Durance, France. The primary goal of ITER was to demonstrate ignition state through the DT experiment, and the planned first plasma in 2021 is delayed due to administrative and engineering issues. The new timeline for the first plasma will be ~2035 if ITER ever finishes construction in time. In recent years, there have been new private-public efforts to accelerate realization of fusion energy development in a much smaller device. They are STEP (https://step.ukaea.uk/) program in the UK and ARC of CFS (https://cfs.energy/), USA, while conventional approach with a large tokamak is still in progress such as CFETR [5], EU-DEMO [6], and K-DEMO [7].

3.1 Edge confinement improvement (ETB) and magnetic configuration

Early toroidal devices (i.e., mainly stellarator and tokamak) were based on circular magnetic flux surface with a limiter configuration. As an example, a photo of poloidal cross section of a discharge in TFTR is shown in Fig. 1a. Here, a bright yellow glow is due to “ionization,” and this region is a potential source of plasmas from limiter surface. As shown in the schematic, the last closed-flux surface (LCFS) (i.e., boundary of the plasma) is in direct contact with the limiter surface. The outflow plasmas (red arrows) impinging on the limiter surface interact with limiter material and neutral gas inside the material of the limiter. The plasmas from ionization on the limiter surface must flow back to the LCFS, and the edge region (0.8 < r/a < 1.0) is a mixture of inflow and outflow plasmas as shown in this schematic (bluish color). The connection between LCFS and limiter surface is like an electric “short circuit.” The confinement mode in limiter configuration is characterized as an L-mode (i.e., discharges with low confinement). In early 1980 s, a noncircular magnetic configuration with divertor system was introduced in ASDEX device, Germany [2], together as shown in a photo in Fig. 1b. Here, glows (ionization) toward the divertor surfaces are shown in this photo. In the schematic of diverted plasma, the LCFS is indirectly in contact with the divertor plate through x-point as shown in this figure.

Therefore, inflow and outflow plasmas between LCFS and divert or surface have a finite Z-value instead of Z = 0 (“short circuit”) for limiter case, where Z represents a flow impedance. In this magnetic configuration, a new high confinement mode (i.e., H-mode) through a sudden transition from the L-mode was discovered, and the confined plasma energy was twice as high compared to that of the L-mode on average [2]. Empirically, a distinctive characteristic of the H-mode discharge was a high edge pressure pedestal and leveled as edge transport barrier (ETB) compared to that of the L-mode discharge as shown schematically in Fig. 1c. Classification of the H-mode is based on higher edge pressure pedestal (ETB) accompanied by dithering spikes in H_α-light (e.g., edge localized mode (ELM) burst) in general.

As discussed in the previous section, the difference in energy confinement time between the L- and H-modes was a factor of 2 on average. It is possible that the formation of the H-mode may arise from a sudden transition from the L-mode phase, and, similarly, the H-mode phase may transition back to the L-mode phase. Whether the toroidal device relies on limiter or divertor, conditioning of the contact surfaces of the limiters or divertors is a routine process of plasma operation. Carbon-based materials have been commonly used for the limiter and divertor surfaces. The goal of conditioning the contact surfaces is the reduction of inflow plasmas including impurities. The process consists of discharge cleaning with RF or low-power discharge cleaning (bombarding plasmas on the surface) as well as surface coating with materials with atomic numbers less than carbon such as beryllium, boron, or lithium. As the detention of tritium in porous carbon-based materials becomes a regulatory problem in ITER, nonporous high Z materials such as tungsten were introduced to avoid the tritium detention problem. The collapse of discharges due to the accumulation of tungsten in the core of the plasma experienced on the Princeton Large Torus (PLT) [8] was revived. It seems inevitable that the introduction of argon or neon seeding (massive gas injection) would be necessary to cool down the outflow plasmas below ~30 eV in order to suppress the ionization of the tungsten. As a result of massive gas injection near the divertor surface, it is inevitable to avoid performance degradation due to the increasing inflow plasmas. This process of massive gas injections may become a bigger problem as the device size increases.

The formation of ETB has been attributed to turbulence suppression mechanisms via the E_rxB effect in the pedestal region. The measurement of E_r at the edge of the H-mode plasmas has been reported in many devices, but the source of the E_r was attributed to the ion orbit loss in the vicinity of the x-point [9]. An alternative source of E_r inside the LCFS can be a response to external E-fields from ∇B drift in the vicinity of the x-point where B_P≅0 as shown in Fig. 2a. The induced E_r inside the LCFS would then spread poloidally through rotational transform. Here, the “flow impedance” which is similar to electrical impedance than fluid impedance can be defined as follows:

Improved confinement in the core is characterized as a peaked pressure profile for ions and electrons with a steep pressure gradient labeled as an internal transport barrier (ITB) as shown schematically in Fig. 4a. In this figure, pressure profiles of one with narrow ITB and another profile with broadened ITB and ETB are illustrated. Note that the core beam fueling and/or core heating has been universal in core confinement improvement for toroidal devices regardless of the edge magnetic configuration (i.e., divertor and limiter). The edge condition that can influence effectiveness of the core heating is an optimum edge density for wave coupling requirements of RF heating and a lower edge density (i.e., control of inflow plasmas) for core heating beam penetration. Representative examples include a peaked ion pressure (T_i>T_e) of the “supershot” in TFTR [19] as shown in Fig. 4b [20] and the peaked electron pressure (T_e>T_i) of the plasma heated by higher harmonic radio frequency (HHRF) on NSTX [21] as shown in Fig. 4c.

Note that the confinement regime with ITB has been observed in plasmas regardless of the edge magnetic configuration (i.e., limiter or divertor). Examples of improved core confinement discharges with the PNB system include the “supershot” and enhanced reversed shear (ERS) discharges [22] in limiter plasmas on TFTR. In divertor plasmas, examples include ITB discharges [23] or the FIRE mode in KSTAR [24], the hot ion mode in DIII-D [25] and JET [26], and the high β_P regime in JT-60U [27]. It is not surprising to find a similar peaked ion pressure profile in different devices, since the beam line arrangement in most devices has almost identical tangential beam lines (i.e., TFTR, DIII-D, and KSTAR) except JT-60U. Since the main power was injected by perpendicular beam lines on JT60-U, high-performance plasma was obtained when the plasma position and size were compromised to have an effective core heating with intense divertor conditioning [27, 28] as shown in Fig. 5a.

As the H-mode confinement regime casts hope for a smaller fusion device than the device based on L-mode discharges, the plasma regimes with both ITB and ETB are even more promising for ignited plasma in a smaller magnetic fusion device. In this regard, a shaped plasma with divertor configuration has advantages over the circular plasma with limiter. They are control of inflow plasmas and flexible geometric factors for access of heating beam such as elongation, triangularity, and reverse D-shape. An example of such confinement mode with both ITB and ETB is “super H-mode” observed in a PNB-heated plasma (DIII-D) and ICRF-heated plasma (C-MOD) [29] as shown in Fig. 5b and 5c, respectively.

Since the ITB formation is common for plasmas in both divertor and limiter setups, it is reasonable to understand that the ITB formation may not be directly associated with the edge magnetic configuration, and it is likely associated with actuators such as an effective localization of the core heating source. It is imperative to establish practical actuators for ETB and ITB through comprehensive understanding so that global energy confinement can be further optimized and controlled in a given geometry.

4.1 C. Auxiliary heating systems in toroidal devices

Toroidal fusion devices need auxiliary heating to increase the core ion temperature well above ~10 keV for optimum fusion reaction condition of DT plasmas. Ultimately, core heating with α-power will be the only heating source in ignited plasmas, and there are two heating systems to generate sufficient α-power; they are ion or electron heating systems. In principle, the heated plasma species (ions or electrons) will exchange energy with each other, and the temperature is expected to be equalized in an equipartition time scale (T_eq~T_e^3/2/n_e). The condition for equalized temperature in ignited plasmas could be n_e >> ~2 × 10²⁰ m⁻³ as illustrated in Fig. 5c. Then, there is no distinction between heating system except engineering issues and required power levels. In this figure, pressure profiles of “super H-mode” plasmas heated with PNB (Fig. 5b) and ICRF (Fig. 5c) are illustrated. In the plasmas heated by PNB and ICRF, the ratio of T_e/T_i~0.5 at n_e~0.8 × 10²⁰ m⁻³ and T_i/T_e~0.85 at n_e~2.0 × 10²⁰ m⁻³, respectively. The gap between ion and electron temperature can be reduced by increasing the operating plasma density. Note that the operating density can be increased using high plasma current and/or magnetic field but decreases as the size is increased. It is important to review experimental results for the optimum choice of heating path to ensure sufficient α-power generation.

The ion heating system has two branches. The first involves direct ion heating through charge exchange with a low-energy positive neutral beam (PNB). The second involves heating a high-energy tail via negative neutral beam (NNB) with beam energy above ~250 keV and ion cyclotron resonance heating (ICRH) via resonance or direct damping of the wave energy. Among ion heating systems, NNB and ICRF are efficient in increasing the electron temperature even though they primarily heat ions, since the fast ions at the high beam energy (> 250 keV) lose energy primarily to electrons as demonstrated in LHD plasmas. Only the PNB system increases bulk ion temperature effectively, and practically speaking, the highest beam energy can be ~120 keV. There is ample experimental data with the direct ion heating system, and the highest α-power generated by the ion heating system was close to ~5 MW. Correlation between the core PNB heating and/or fueling and improved core confinement was extensively studied in TFTR plasmas [30, 31]. Here, a designed scaling study of the global confinement time of the plasmas heated by PNB with beam energy of ~100 keV including “supershot” regime showed that τ_E is linearly proportional to the peakedness of beam fueling profile [30]. The peakedness of the beam fueling profile is defined as a ratio of core beam fueling and volume averaged beam fueling. Data from high-β_P regime in JT-60U [27] was well aligned with the “supershot” data from TFTR [32]. The core confinement was further improved by radially expanding the ITB position up to r/a~0.6. The T_i profile with the highest performance discharge in JT-60U [33] is shown in Fig. 5a. Here, the position and size of the plasma were compromised so that one of the perpendicular beam lines was aimed at the center while the other one was aimed at r/a~0.25 [28], while an extremely low edge density was sustained as shown in Fig. 5a. Another example is the “super H-mode” [29] on DIII-D, which was obtained with a combination of tangential beam lines and an off-axis PNB system as shown in Fig. 5b. It was shown that direct ion heating is extremely effective in increasing ion temperature above ~10 keV, but electron temperature is saturated in all discharges with high ion temperature as shown in the “supershot” (Fig. 4b) and super H-mode (Fig. 5b).

If the choice of heating is PNB system which has demonstrated achieving high ion temperature, the initial plasma with T_i/T_e > 1 at moderately high density can switch to ignited plasmas with higher density through DT fueling so that electron heating by α-particles can thermalize fast to sustain T_i~15 keV. At the same time, a gate valve with sufficient neutron shielding can block the access of PNB beam lines.

It is critical to understand the electron heating process to reach the ion temperature optimum for ignition state (T_i > 10 keV), since α-particle power at 3.5 MeV is the only heating source once the ignited plasma state is established by the external heating. In electron heating experiments, similarly peaked T_e profiles were observed in numerous heating experiments by ECRH [34]. Examples of radiofrequency (RF) heating are HHRF [21] heated plasmas in NSTX (Fig. 4c) and ICRF-heated plasma in C-MOD as shown in Fig. 5c. In both figures, it is evident that there is a signature of core density pump-out during the RF heating period. The electron heating system is based on the dissipation of wave energy through resonance like low-hybrid heating (LH) and ECRH [35]. Empirically, in plasmas with electron heating systems (LH and ECRH), the electron temperature is increased, while the ion temperature is clamped at the lower temperature compared to that of the electron (T_i<<T_e) [36]. The observed density pump-out and clamping of T_i problem in electron heating system are serious issues.

If there is any experimental experience at higher electron heating power > 10 MW or a plasma with Ti > 10 keV, it would be easier to estimate the power level to reach the ignition state. Any device based on an electron heating system may have to prepare up to ~50 MW, since the power level used in PNB was ~40 MW and ~50 MW α-power would be sufficient to test the ignition state. Thus, it is also important to consider how to deliver such high power to the plasma.

4.2 D. Transport models for ITB and ETB and experimental data

Among numerous transport models for ITB, a few popular models will be examined, with attention paid to consistencies and inconsistencies in the experimental results. Following discovery of the “supershot” in TFTR [20], similar improved discharges with similar and different ITB positions and pressure profile shapes have been reported with various names, as if it is unique for each device. Considering each device has different beam line arrangements, beam energy, plasma shape, and density profile, it is not surprising that the ITB position ranges from r/a = 0.3 to 0.6. Note that the improved core confinement with high ion (or electron) temperature can be achieved as long as the heating power is deposited in the vicinity of the core region of the discharges in both L-mode and H-mode edges as discussed in the previous section. ITBs in ICRF and ECRH heated discharges are within r/a~0.2 except a broad ITB and ETB in C-MOD as shown in Fig. 5c.

Interpretation of the improved confinement with edge pedestal formation (ETB) and steep pressure gradient near the core (ITB) is mostly based on turbulence suppression mechanisms due to the pressure gradient condition, velocity shearing rate, and core region q-profile shape deviating from monotonic profile. (1) The first example could be the η_i(=L_ne/L_Ti) marginality condition in ITG mode suppression [37] where L_ne is the density and L_Ti is the ion temperature scaling length, respectively. The condition of the ITG mode suppression for the “supershot” was η_i~3–5, and this value was more or less the same for the measured profiles of the “supershot” case. As experimental data was accumulated, a wide range of measured values for η_i was observed. For example, even it can be infinite for the broadened ITB in “super H-mode” case where the density profile is flat as shown in Fig. 5b. (2) The second example comes from various core magnetic shear from weak shear to reverse shear. There are many reports on the improved core confinement (peaked ion pressure profile) based on the shear of the q-profile, and q-minimum position coincides with the position of ITB [3, 38]. Note that the q-profile shape in the core can easily be modified via a driven heating beam current. Isolation of the ITB position from modified q-minimum position due to heating beam current [39] should be clarified, in order to validate the causality. (3) The most popular example is turbulence suppression due to poloidal rotation profile shear of the plasma arising from E_rxB effect. An example of ITB formation due to this mechanism in the core [22] and edge region for ETB formation [40] shares the same basic idea. The improved confinement is through the breaking of semi-coherent turbulence structures such as streamers and ITG mode which are thought to be responsible for a rapid loss of plasma energy as demonstrated through simulation [41]. Note that measurements of poloidal shear, E_r and identification of turbulence in the core (Fig. 6) are non-trivial, and reliable data are limited. E_r well inside the LCFS of the H-mode has been confirmed by numerous measured E_r at the edge of the plasmas [45, 47]. Theoretical prediction of E_r well was given based on ion orbit loss near x-point using gyrokinetic simulation [42], and the prediction was consistent with the measurement in most of the H-mode edge experiments. In a comparative experimental study of positive triangularity (PT) and negative triangularity (NT), edge confinement of the H-mode edge in PT was higher than that of the NT on AUG [14] as shown in (Fig. 8) of this reference. The core confinement of NT on TCV [14] was higher than that of PT when PNB was used, and this difference may be due to effective core heating in NT. The recent comparative gyrokinetic simulation of ion orbit loss in the geometry of NT and PT reported that the E_r well in NT is higher than that of PT [9]. Therefore, improved edge confinement is expected in NT configuration rather than PT configuration.

A potential alternative source of E_r inside the LCFS in H-mode can be due to the external E-field induced by ∇B drift of the plasmas in the vicinity of the x-point where the poloidal field (B_P) is close to zero as shown in Fig. 2. This is similar to the classical ExB effect on the equilibrium of the toroidal plasma without poloidal field. Inside the LCFS region close to the E-field, electrons accumulated in response to the positive charges outside the LCFS resulting in a negative E_r. The induced E_r will spread to the same flux zone through helicity, while the external E-field will be confined in the vicinity of the x-point. This ExB drift of the plasmas between LCFS and divertor may be responsible for the observed high density and high turbulence level in the outer-leg of the divertor region [45]. In visible images of the divertor system, it is common that the intensity of the outer leg is brighter than that of the inner leg.

There is an excellent review of many experimental measurements of turbulence and E_r at the pedestal as well as the scrape-off layer (SOL) in the edge plasmas [46]. In general, the frequency spectra have bandwidth < ~1 MHz, and dominant low frequency is universal as long as Doppler shift due to plasma rotation is corrected and long wavelengths are dominant. Both frequency and wavelength spectra are more or less the same for all measurements in toroidal devices.

A full profile of turbulence measured by BES and reflectometry in a “supershot” discharge which has ITB in the core density and T_i profiles and edge of extremely well-conditioned limiter plasmas in TFTR is illustrated in Fig. 6a [46]. A high-level turbulence (ñ(r)/n(r)~20%–30%) at LCFS rapidly drops to ~2~3% level at about r/a = 0.9. Then, a rapid decrease of (ñ(r)/n(r)) from ~2~3% to ~0.4% near the core is illustrated in Fig. 6b, and this is largely due to peaked density profile in “supershot” discharge as shown in Fig. 6b. The unnormalized ñ(r) profile is almost flat for the region of r/a < ~0.8, and the absolute value of ñ(r) is ~1–2 × 10¹⁷/m³ with a large uncertainty. The ñ(r) increases rapidly considering the mild density gradient in the edge as shown in Fig. 6b. The excess part of density turbulence (ñ(r)) can be attributed to inflow turbulence from the limiter. Note that the beam fueling rate is ~10¹⁷/m³ s in the core region, and one neutral beam ion carries one cold electron.

There are many papers on the measurement of edge turbulence and different suppression mechanisms for improved confinement at the edge region [45]. However, there is no local measurement of relevant plasma parameters in the vicinity of the x-point, and measurements are near the midplane. Therefore, quantities like inflow/outflow plasma density and turbulence can be highly asymmetric. An excellent example of turbulence suppression due to the E_rxB effect with full set of profiles in a diverted plasma (DIII-D) will be examined. A comparative study is given with the measured profiles of density, turbulence, E_r, and velocity shear at the edge (r/a = 0.85–1.0) [47] and SOL region (r/a > 1.0) [48] of the L-mode and ELM-free H-mode phase in quiescent Ohmic plasmas. As shown in the reduced set of data in Fig. 7, the correlation between the normalized turbulence level (ñ(r)/n(r)) and density profile at the edge of the L- and H-mode phase represents a clear suppression of turbulence due to V_ErxB in H-mode phase. In the L-mode phase, the level of the ñ(r)/n(r) is ~20–30% higher than that of the H-mode phase at the LCFS region and gradually merges to the H-mode level at r/a = 0.85 as shown in Fig. 7b. This result can be paired with the measurements in SOL region as shown in Fig. 7e. In the L-mode phase, ñ(r)/n(r) is 20~30% at the LCFS and is almost constant across the SOL. In the H-mode phase, ñ(r)/n(r) starts with the same magnitude as the L-mode before briefly dropping by a of factor 0.5 that of the L-mode briefly and increases significantly. Note that measuremental error at a low density can contribute to this nonlinear behavior. The plasma density profiles in both L- and H-mode in SOL are continuation of the measured edge density at the LCFS (i.e., significantly higher density with long scale length in L-mode phase while extremely low density in H-mode phase).

It is important to investigate what happens to the plasma turbulence amplitude and spectra when the large-scale structure of turbulence is torn apart due to velocity shear or equivalent mechanisms. If the breaking of turbulence structures like streamer and ITG modes by the E_rxB effect is responsible for reduced transport at the pedestal region, it is natural that the wave amplitude should be decreased in the region where the confinement is improved or vice versa. The nature of turbulence in plasma is wave-like, and the turbulence spectra can be represented as a superposition of all different wave numbers and frequencies as shown in Eq. 3.

5.1 Energy confinement time scaling laws for design of tokamak plasmas

One of the key performance measures of toroidal devices is the energy confinement time [τ_E = stored energy (J)/heating power (P_H)]. Following a series of empirical studies of τ_E (mainly tokamaks and stellarators), scaling laws for τ_E were established with worldwide experimental data. The scaling study is a statistical regression study of the measured stored global energy confinement time against various device and plasma parameters, including the geometric factors as follows: major radius (R), minor radius (a), elongation (κ) and triangularity (δ), heating power (P_H), plasma current (I_P), plasma density (n_e), and magnetic field (B_T). For reliable statistical study, experimental designs with uncorrelated independent parameters are prerequisite. However, it is extremely difficult to interpret parameters as being dependent in real data. The degree of intercorrelation between independent parameters can easily change the exponents of independent parameters. Finally, a credible energy confinement time scaling law (ITER-89P scaling) [49] was established from L-mode data of worldwide tokamak devices before 1990 as shown in Eq. 4.

6.1 Perspective of ignition in magnetic fusion

Among magnetic fusion devices, closed system such as tokamaks and stellarators is more favored over open system like magnetic mirror, due to their better performance in energy confinement in general. The intrinsic energy loss mechanism in an open system such as the axial loss in the mirror device is difficult to overcome. Among closed magnetic devices, performances of tokamaks and stellarators showed more promise than others such as field-reversed configuration (FRC) or spheromak. As discussed in earlier sections, core improved confinement (ITB) of the closed magnetic surface shares the same actuator (i.e., heating profile), but edge confinement can be different with different edge magnetic configurations (i.e., single to multiple x-points). The edge confinement of tokamak plasmas has an advantage (i.e., high flow impedance) over stellarators (i.e., low flow impedance) unless the system can deduce the x-points. Stellarators do not require a driven plasma current, while tokamaks and other closed devices require a plasma current (poloidal or toroidal) to achieve equilibrium. But this very plasma current for stable equilibrium can also induce harmful MHDs and lead to disruption. For continuous operation of these devices, an external current source is required. If the goal is a demonstration of ignition plasma in a magnetic fusion, tokamaks may be the best choice for now. Note that superior energy confinement of the tokamak approach undermines issues of instability and current drive which are essential for steady-state operation. For this issue, the stellarator configuration that does not depend on plasma current has potential for achieving steady state in fusion devices if the inferior confinement issue (i.e., poor edge magnetic configuration) and complexity of hardware can be resolved.

After three large tokamak eras, devices based on superconducting magnets such as KSTAR, EAST, and LHD and W7-X were constructed to challenge a steady-state operation expecting an efficient external current drive source which has yet to come for tokamaks. The initiation of an international effort (i.e., ITER) to go beyond scientific breakeven took a long time. The current ITER project to demonstrate an “ignition state” and a “tritium breeding test” is in progress, but future perspectives depend on resolving uncertainties of electron heating and engineering issues. Now fusion energy development efforts by private sectors are active, with representative ones including CFS/MIT, USA, and Fusion Energy, UK. A plasma device size comparable to JET class (V_P~90 m³) may not be able to achieve the ignition, and even devices like ARC and JT60-SA (V_P~140 m³) may only marginally achieve the ignition state due to short falls in energy confinement time. Most large fusion devices like K-DEMO [7], EU-DEMO [6], and CFETR [5] including ITER have been designed with the plasma volume more than V_P~900 m³ and may have potential in surpassing the ignition state, but there is no clear path for high plasma density operation at ion temperature above ~10 keV with electron heating systems such as ECRH and ICRF in such a large device.

6.1.1 Most probable ignition test device for magnetic fusion

The first step would be estimation of a plasma volume for fusion power which can produce sufficient α-power to sustain the ignition state. The plasma volume is based on the energy confinement time scaling as demonstrated in the previous section. The target τ_E can be ~2.4 s assuming the discharge has an enhancement factor (H-factor) of ~1.5. Then, the equivalent H-mode confinement time (i.e., ITER-98) is ~1.6 s. Using the plasma volume (V_P~90 m³) of the JET device which has a median value of τ_E~0.6 s as shown in Fig. 8, the equivalent plasma volume (V_P) can be ~240 m³. Note that the plasma volume can be further reduced to ~180 m³ if a long confinement time (~0.9s) in JET data and a high-density operation is adapted.

Second, design of optimum ion heating systems (combination of on-axis and off-axis beam lines) for effective core heating to achieve the best H-factor possible as well as high ion temperature. Good references are high-performance discharges demonstrated in JT-60U and the “super H-mode” in DIII-D. In a moderately large plasma (i.e., V_p < 300 m³), optimization of core heating can be achieved utilizing plasma geometric factors, edge density, and injection angles of PNB system. In the early design phase, various shapes of equilibrium (i.e., D-shape and reverse D shape with high elongation and racetrack) should be considered without compromising essential edge magnetic configuration. The choice of the plasma minor radius (a~1.2 m) is only slightly larger than that of the JET device where ~90-keV PNB was successfully used for improved core confinement regime (T_i>T_e). Therefore, PNB power up to ~40 MW at the beam energy of ~120 keV can be a good target. The heating beam source at ~120 keV with minimum 1/2 and 1/3 energy components would help the core heating. For effective core heating at high-target density plasmas, the injection angles and plasma geometry can be optimized. An extensive MHD stability study for stable pressure profiles should be performed to accommodate optimum core heating.

Finally, the most important task is controlling the pedestal density of the plasma through a smart divertor system so that a high edge confinement mode is sustained while core heating is allowed. Note that the density limit in tokamak plasmas is purely empirical (i.e., Murakami limit, Greenwald limit). Operation of the plasma density ~1.5 × 10²⁰/m⁻³ in moderate plasma volume (~240 m³) is a reasonable approach, since the core density of the “supershot” in TFTR was >~1 × 10²⁰ m⁻³. The initial ignition state can be reached at a slightly low density with external heating, while α-power is increasing. Once the ignition state is achieved, fueling rate can be slowly increased while the PNB system can be closed.

Using τ_E~2.4 s, n_e~1.5 × 10²⁰ m⁻³, and T_i~15 keV (Q~5–6 with PNB power of ~40 MW), the initial fusion power will be ~220 MW with an α-power of ~45 MW which may be adequate to test the initial ignition state with ion temperature ~15 keV. Note that these numbers are for guidance purposes only, and there will likely be deviations from operating plasma pressure and external heating power. Additionally, there is large uncertainty with respect to transition of external and internal heating source, and the α-power of ~45 MW may be a very conservative side. Also, an improved H-factor above ~1.5 can provide more fusion power ~300 MW at smaller device size (V_P < 200 m³). A successful operation of the ignition state warrants demonstration of electricity generation so that the fusion energy can be a potential practical energy source for mankind.

The concept of flow impedance, based on inflow/outflow plasmas between the LCFS and divertor, qualitatively explains edge confinement characteristic of tokamaks and stellarators. The interplay between inflow and outflow plasmas thus may be responsible for the edge of the L-mode and H-mode as well as transitions between two modes. Here, the turbulence part of the inflow plasmas from a divertor may provoke cross-field anomalous transport of the outflow plasmas, and density part contributes to the edge plasma density. Similarly, EHO or Alfven modes at the edge of QH-mode and I-mode can play a similar role of turbulence. A smart divertor system design is critical for control of turbulent inflow plasmas and effective heat dissipation as an edge control actuator. The actuator for core confinement can be an effective core heating system for ions until issues of electron heating system are resolved. The plasma volume is primarily determined by energy confinement time scaling study, and direct ion heating with PNB power of ~40 MW will be effective in sustaining plasmas with T_i > 10 keV at moderately high plasma density of ~1.5 × 10²⁰/m³. The most probable compact tokamak plasma with volume of ~240 m³ can validate transition physics from external heating to α-heating as suggested. The fusion power estimated to reach ~220 MW (Q~5–6) with an α-power of ~45 MW, thus demonstrating a potential electricity output of ~100 MW.