# High-confinement mode

In plasma physics and magnetic confinement fusion, the high-confinement mode (H-mode) is a phenomenon and operating regime of enhanced confinement in toroidal plasma such as tokamaks. When the applied heating power is raised above some threshold, the plasma transitions from the low-confinement mode (L-mode) to the H-mode where the energy confinement time approximately doubles in magnitude. The H-mode was discovered by Friedrich Wagner and team in 1982 during neutral-beam heating experiments on ASDEX. It has since been reproduced in all major toroidal confinement devices, and is foreseen to be the standard operational scenario of ITER.
In H-mode, the change in confinement is the most apparent at the edge of the plasma where the pressure gradient increases rapidly due to the increase in edge density, leading to the formation of a pedestal-like structure in the radial profile of the plasma parameters. It also typically features a type of magnetohydrodynamic instability called the edge-localized modes (ELMs), which appear as periodic bursts of particle and heat flux and can potentially cause excessive heating of plasma-facing components.
The physical origin of H-mode is currently unclear. The improved confinement is believed to be related to significantly reduced plasma turbulence at the edge. A possible explanation concerns increased flow shear which suppresses turbulent transport at the plasma edge.

## Energy confinement scaling
### L-mode scaling

From the fusion triple product it is known that both temperature and energy confinement time of the fusion fuel must be high enough for fusion ignition. It was however found 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. The L-mode is characterized by relatively large amounts of turbulence, which allows energy to escape the confined plasma. The energy confinement time $\tau _{E}$ for tokamak L-mode is given empirically by the ITER89-P scaling expression:
    $\tau _{E}^{\text{ITER89-P}}=0.038M^{0.5}I_{\text{P}}^{0.85}R^{1.5}\epsilon ^{0.3}\kappa ^{0.5}n^{0.1}B^{0.2}P^{-0.5}$
where
* $M$ is the hydrogen isotopic mass number
* $I_{\text{P}}$ is the plasma current in ${\text{MA}}$
* $R$ is the major radius in ${\text{m}}$
* $\epsilon$ is the inverse aspect ratio
* $\kappa$ is the plasma elongation
* $n$ is the line-averaged plasma density in $10^{19}{\text{m}}^{-3}$
* $B$ is the toroidal magnetic field in ${\text{T}}$
* $P$ is the total heating power in ${\text{MW}}$

### H-mode scaling: IPB98(y,2)

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