High-confinement mode, or H-mode, is an operating regime possible in toroidal magnetic confinement fusion devices – mostly tokamaks, but also in stellarators.^[1] In this regime the plasma has a higher energy confinement time.

It was discovered by Friedrich Wagner and his team in 1982 during neutral-beam heating of the plasma at ASDEX.^[1] It has since been reproduced in all major toroidal confinement devices and is planned in the operation of ITER. Its self-consistent theoretical description was a topic of research in 2007.^[2] It was still considered a mystery with multiple competing theories (e.g. predator–prey model) in 2016.^[3]

Background

It is known from the fusion triple product that both temperature and energy confinement time of the fusion fuel must be high enough for fusion ignition. High core plasma temperatures for fusion require auxiliary heating additional to Ohmic heating. Examples of auxiliary heating techniques are neutral-beam injection (NBI), electron cyclotron resonance heating (ECRH), and ion cyclotron resonance heating (ICRH). It was however found that that the energy confinement time scales inversely with applied power. Prior to the discovery of H-mode, all tokamaks operated in what is now called the L-mode, or low-confinement mode. The L-mode is characterized by relatively large amounts of turbulence, which allows energy to escape the confined plasma. The energy confinement time ${\displaystyle \tau _{E}}$ for tokamak L-mode is given empirically by the ITER89-P scaling expression:^[4]

${\displaystyle \tau _{E}^{\text{ITER89-P}}=0.038M^{0.5}I_{\text{P}}^{0.85}R^{1.5}\epsilon ^{0.3}\kappa ^{0.5}n^{0.1}B^{0.2}P^{-0.5}}$

where

• ${\displaystyle M}$ is the hydrogen isotopic mass number
• ${\displaystyle I_{\text{P}}}$ is the plasma current in ${\displaystyle {\text{MA}}}$
• ${\displaystyle R}$ is the major radius in ${\displaystyle {\text{m}}}$
• ${\displaystyle \epsilon }$ is the inverse aspect ratio
• ${\displaystyle \kappa }$ is the plasma elongation
• ${\displaystyle n}$ is the line-averaged plasma density in ${\displaystyle 10^{19}{\text{m}}^{-3}}$
• ${\displaystyle B}$ is the toroidal magnetic field in ${\displaystyle {\text{T}}}$
• ${\displaystyle P}$ is the total heating power in ${\displaystyle {\text{MW}}}$

It was discovered in 1982 on the ASDEX tokamak that when the heating power applied is raised above a certain threshold, the plasma transitions spontaneously into a higher-confinement state where the energy confinement time approximately doubles in magnitude,^[1] albeit still showing an inverse dependence on heating power. This improved confinement regime was called the H-mode, and the previous state of lower confinement was in turn called the L-mode.

Due to its improved confinement properties, H-mode quickly became the desired operating regime for most future tokamak reactor designs. The physics basis of ITER rely on the empirical ELMy H-mode energy confinement time scaling.^[5] One such scaling named IPB98(y,2) reads:

${\displaystyle \tau _{E}^{\text{IPB98(y,2)}}=0.0562M^{0.19}I_{\text{P}}^{0.93}R^{1.97}\epsilon ^{0.58}\kappa ^{0.78}n^{0.41}B^{0.15}P^{-0.69}}$

L-H transition threshold

L-H mode transition

Edge transport barrier

Edge-localized mode

See also

• Edge-localized mode, an instability of H-mode

References