2.1. Transport physics effects

There are numerous basic plasma parameters that depend on the ion mass number. These include the thermal velocity ${v_i} = {( {T_i}/{m_i}) ^{1/2}}$ where ${m_i} = A{m_p}$, ${m_p}$ being the proton mass, the ion Larmor radius ${\rho _i} = {v_i}/{\omega _{\textrm{ci}}}, \;{\omega _{\textrm{ci}}} = ZeB/( A{m_p}) $ being the ion cyclotron frequency, the Alfvén velocity ${v_A} = B/{( {\mu _0}{n_i}{m_i}) ^{1/2}}$, the ion–ion collision frequency ν _ii and electron–ion momentum and energy exchange frequencies ν _ei and $v_{\textrm{ei}}^E$ (for a single ion species plasma).

(2.1a–c)\begin{align} {v_{\textrm{ii}}} = \frac{{{n_i}{Z^4}{e^4}\ln \varLambda }}{{8\sqrt 2 {\rm \pi} \epsilon_0^2 {m_i^2v_i^3} }} \propto {A^{ - 1/2}}, \;\quad {v_{\textrm{ei}}} = \frac{{{n_i}{Z^2}{e^4}\ln \varLambda }}{{8\sqrt 2 {\rm \pi} \epsilon_0^2 {m_e^2v_e^3} }} \propto {A^0}, \;\quad v_{\textrm{ei}}^E = \frac{{2{m_e}}}{{{m_i}}}{v_{\textrm{ei}}} \propto {A^{ - 1}}, \end{align}

as well as the electron–ion heat exchange power density ${q_{\textrm{ei}}} = 1.5{n_e}\nu _{\textrm{ei}}^E( {T_e} - {T_i}) \propto {A^{ - 1}}$. In the above B is the magnetic field, n_i is the ion density, Z the atomic charge number, n_e the electron density, ${v_e} = {( {T_e}/{m_e}) ^{1/2}}$ the electron thermal velocity and ln Λ is the Coulomb logarithm (Huba Reference Huba2013).

We loosely follow Horton (Reference Horton1999) to introduce the basic expectation for the scaling of the cross-field diffusion coefficient D and heat diffusivity χ for drift wave turbulence $D \sim \chi \sim \Delta _r^2/\delta t$, where Δ_r is the characteristic turbulent radial scale length and ${\delta _t} \approx {L_\theta }/{v_d} \approx {L_\theta }/( T/eZB{L_r}) $ its characteristic time scale, ${v_d} = T/( eZB{L_r}) $ the drift velocity with L_r a radial profile gradient length such as ${L_n} ={-} n/{{\bf \nabla }_r}n$ or ${L_T} ={-} T/{{\bf \nabla }_r}T$. Here, L_θ is the poloidal scale length related to the poloidal mode number m as L_θ ≈ 2${\rm \pi}$a/m, where a is the plasma minor radius. This leads to $\chi \sim ( T/eZB) ( \Delta _r^2/{L_\theta }{L_r}) $ and gives rise to different scalings depending on the characteristic lengths scales assumed. Two such assumptions have proven particularly popular, providing fodder for three decades of debates over the nature of plasma turbulent transport. The first of these corresponds to ‘macro-turbulence’ and makes the assumption that all length scales are proportional to the plasma size itself (e.g. the minor radius) and leads to $\chi \propto T/eZB \propto {A^0}$. This diffusivity is called Bohm-like because has the same dependences as the classical Bohm diffusion coefficient (Bohm Reference Bohm, Guthrie and Wakerling1949; Spitzer Reference Spitzer1960). The Bohm diffusion coefficient is a worst case estimate obtained by assuming ${\delta _t} = \omega _{\textrm{ci}}^{ - 1}$ and ${\Delta _r} = {\rho _i}$. We wish to emphasise here that, despite their identical dependences on temperature and magnetic field, Bohm and Bohm-like diffusion belong to very different theoretical frameworks, the former making no reference to drifts, let alone drift waves and turbulence. GyroBohm scaling, $\chi \propto ( T/ZeB) ( {\rho _i}/R) \propto {A^{1/2}}$, follows from the assumptions ${\Delta _r} \sim {\rho _i}$, ${L_\theta } \sim {\rho _i}$ and ${L_r} \sim a \propto R$, as expected for quasi-isotropic ion scale drift wave turbulence, i.e. ITG and trapped electron mode (TEM) turbulence. Equivalently, gyroBohm scaling can be obtained from a mixing length estimate, $\chi \approx \langle \gamma /k_ \bot ^2\rangle$, with ${k_ \bot } \propto 1/{\rho _i}$ and the growth rate $\gamma \propto {k_ \bot }{v_d}\,f( {L_{\textrm{Te}}}, \;{L_{\textrm{Ti}}}, \;{L_n}, \;{\nu _{\textrm{ei}}}, \;{T_i}/{T_e} \ldots ) $ if the complex dependencies in f are ignored (Horton, Choi & Tang Reference Horton, Choi and Tang1981; Waltz Reference Waltz1985; Horton Reference Horton1999; Bourdelle et al. Reference Bourdelle, Citrin, Baiocchi, Casati, Cottier, Garbet and Imbeaux2016).

Early experiments were at odds with gyroBohm scaling not only in the context of isotope dependencies: Experiments in DIII-D L-mode deuterium plasmas where species resolved transport investigations were performed showed ${\chi _i}\propto \rho _i^{ - 0.5}$ i.e. opposite in sign to gyroBohm, while the electron diffusivity scaled as ${\chi _e}\propto {\rho _e}$ (Petty et al. Reference Petty, Luce, Pinsker, Burrell, Chiu, Gohil, James and Wroblewski1995). GyroBohm scaling does remain the fundamental underlying scaling for both quasi-linear and nonlinear gyrokinetic physics in the local, electrostatic, collisionless, flowless limit with adiabatic electrons, as shown in nonlinear GYRO simulations (Pusztai, Candy & Gohil Reference Pusztai, Candy and Gohil2011). These have resulted in nonlinear heat fluxes that do indeed closely follow the expected scaling, $Q/Q_{\textrm{gB}}^\textrm{H}\propto {A^{ - 1/2}}$. The result is consistent with Rosenbluth–Hinton zonal flows (Rosenbluth & Hinton Reference Rosenbluth and Hinton1998), which have radial scales larger than the trapped ion widths and retain gyroBohm scaling of heat fluxes also in the nonlinear saturated stage. However, as seen in advanced modelling and in experiment, the above mentioned neglected physics can modify the basic gyroBohm scaling beyond recognition.

The first mechanism discovered to be capable of causing deviations from gyroBohm scaling is most likely E × B shear flow stabilisation (Hahm & Burrell Reference Hahm and Burrell1995; Waltz et al. Reference Waltz, Dewar and Garbet1998). Such E × B shear flow may arise e.g. from sheared toroidal rotation due to momentum injection by NBH. It is also intrinsic to the formation of zonal flows (Rosenbluth & Hinton Reference Rosenbluth and Hinton1998; Diamond et al. Reference Diamond, Itoh, Itoh and Hahm2005; Hahm et al. Reference Hahm, Wang, Wang, Yoon and Duthoit2013; Bustos et al. Reference Bustos, Bañón Navarro, Görler, Jenko and Hidalgo2015) which damp/regulate the turbulence level in its developed, nonlinear state. The mechanism leads to turbulence quenching when the rotational flow shear rate exceeds the growth rate of the instability. It was not initially invoked for explaining isotope effects, however, we can see from a quasilinear estimate of ion heat diffusivity χ_i how an isotope dependence may arise from it. From $\gamma _{\textrm{max}}^i = \gamma _{\textrm{max}}^\textrm{H}{A^{ - 1/2}}$and hence $\chi _{\textrm{gB}}^i = \chi _{\textrm{gB}}^i{A^{1/2}}$ it follows

(2.2)\begin{equation}{\chi _i} \propto \chi _{\textrm{gB}}^i\left({1 - \alpha \frac{{{\omega_{E \times B}}}}{{\gamma_{\textrm{max}}^i}}} \right)= \chi _{\textrm{gB}}^\textrm{H}{A^{1/2}}\left({1 - \alpha \frac{{{\omega_{E \times B}}}}{{\gamma_{\textrm{max}}^\textrm{H}}}{A^{1/2}}} \right), \end{equation}

where ω_{E ×B} is the shearing rate, which may arise from gradients of the toroidal velocity or from ion temperature gradients (see e.g. Ernst et al. Reference Ernst, Coppi, Scott and Porkolab1998), γ _max is the growth rate of the fastest growing mode and α a parameter describing the strength of shear flow stabilisation. For $\alpha^\ast= \alpha \omega _{E \times B}/\gamma _{\textrm{max}}^\textrm{H} = 0$, there is no stabilisation, for $\alpha^{\ast} \gt 0.36$, ${\chi _\textrm{T}} \lt {\chi _\textrm{H}}$ as sketched in figure 1 and for $\alpha^{\ast} = 0.58$ there is complete suppression for tritium, but not for hydrogen and deuterium (where H, D and T stand for hydrogen, deuterium and tritium respectively). Hence the E × B effect may lead to an isotope effect opposite to gyroBohm both for E × B resulting from sheared bulk rotation and via zonal flows (Bustos et al. Reference Bustos, Bañón Navarro, Görler, Jenko and Hidalgo2015). It should hence be noted that deviations from gyroBohm scaling do not imply that the transport is not governed by ion scale turbulence (e.g. by macro-turbulence if a Bohm-like scaling, ${\chi _i}\propto {A^0}$, is observed). We also note that in ‘real world’ situations, the simple picture of (2.2) is likely to be complicated by the fact that ω_{E ×B} itself, whether from zonal flows or externally imposed, is likely to also depend on the isotope mass.

Figure 1.

Sketch to illustrate (2.2). Isotope dependence of shear flow stabilisation for 3 values of $\alpha^{\ast}= \alpha {\omega _{E \times B}}/{\gamma _{\max }}$, assuming gyroBohm scaling for underlying transport (α* = 0).

The E × B shear flow stabilisation was credited for stabilising turbulence in the H-mode edge transport barrier (Biglari Reference Biglari, Diamond and Terry1990; Hinton Reference Hinton1991) and in enhanced core confinement regimes such as the H-mode pedestal, VH (very high confinement) modes in DIII-D and TFTR supershots (Hahm & Burrell Reference Hahm and Burrell1996). In TFTR L-modes and supershots, E×B shearing was used to explain the not only improved confinement, but also the observation of stronger confinement improvement for D–T mixtures over pure D plasmas (Scott et al. Reference Scott, Zarnstorff, Barnes, Bell, Bretz, Bush, Chang, Ernst, Fonck and Johnson1995; Ernst et al. Reference Ernst, Coppi, Scott and Porkolab1998). However, with hindsight, other mechanisms, which were not yet discovered at the time, must have played a role too in these enhanced core confinement regimes.

Analytical work by Hahm et al. (Reference Hahm, Wang, Wang, Yoon and Duthoit2013) with kinetic particles showed that finer scale zonal flows (narrower than the ion banana width) can lead to reduced transport with respect to gyroBohm scaling for the heavier isotopes. This was confirmed in nonlinear simulations using the gyrokinetic code GENE (Jenko et al. Reference Jenko, Dorland, Kotschenreuther and Rogers2000; Görler et al. Reference Görler, Lapillonne, Brunner, Dannert, Jenko, Merz and Told2011), which exhibited notable deviations from gyroBohm scaling in TEM and mixed TEM/ITG turbulent plasmas with T_i/T_e = 1, with ${Q^\textrm{T}}/Q_{\textrm{gB}}^\textrm{T}/( {Q^\textrm{H}}/Q_{\textrm{gB}}^\textrm{H}) \sim 0.82$ (Bustos et al. Reference Bustos, Bañón Navarro, Görler, Jenko and Hidalgo2015). The reduction of heat flux with isotope mass was attributed to a stronger zonal flow stabilisation of the turbulence at higher isotope mass, with ω_{E ×B}/γ _max increasing with isotope mass. A similar behaviour is observed when TEM turbulence is stabilised by electron–ion collisions: near marginality, the role of zonal flows in turbulence regulation is enhanced and this more strongly at high isotope mass (Nakata et al. Reference Nakata, Nunami, Sugama and Watanabe2017). This effects adds to the linear stabilisation of TEM by collisions which scales as ${v_{\textrm{eff}}}\sim {v_{\textrm{ei}}}/{\gamma _0}\propto {A^{1/2}}$, where γ ₀ is the collisionless growth and is therefore stronger at high isotope mass (Angioni et al. Reference Angioni, Fable, Manas, Mantica and Schneider2018). Nonlinear GENE (Jenko et al. Reference Jenko, Dorland, Kotschenreuther and Rogers2000; Görler et al. Reference Görler, Lapillonne, Brunner, Dannert, Jenko, Merz and Told2011) simulations by one of the authors (M. Oberparleiter) in the course of the isotope effect investigations in JET (Maggi et al. Reference Maggi, Weisen, Hillesheim, Chankin, Delabie, Horvath, Auriemma, Carvalho, Corrigan and Flanagan2018; Weisen et al. Reference Weisen, Maggi, Menmuir, Horvath, Bache, Casson, Oberparleiter, Saarelma, Auriemma and Chankin2018) confirmed this mechanism is also active in ITG dominated turbulence and will be presented in detail later in the paper. A reversal of gyroBohm scaling has also been linked to the electron-to-ion mass ratio dependence of the non-adiabatic electron response when the turbulence is strongly influenced by the electron parallel dynamics (as for TEM and for the highly collisional plasma edge) (Belli, Candy & Waltz Reference Belli, Candy and Waltz2019; Bonanomi et al. Reference Bonanomi, Angioni, Crandall, Di Siena, Maggi and Schneider2019a).

Electromagnetic effects can lead to an isotope effect as well through a nonlinear process as demonstrated for an ITER case in DD vs DT. Whereas linear simulations do not show a departure from gyroBohm scaling, at high beta the ion heat flux decreases with increasing mass due to a nonlinear interplay between zonal flows, electromagnetic effects and mass (Garcia et al. Reference Garcia, Görler, Jenko and Giruzzi2017). Such a deviation from gyroBohm scaling is enhanced in plasma conditions of high beta and high E × B shearing, as expected in advanced tokamak scenarios with high NBH power. In the particular case of DD vs DT plasmas, the additional fast ion contribution from the alpha particles from DT reactions can further reduce the ion heat flux by fast ion electromagnetic stabilisation resulting in considerable de-stiffening of the ITG mode, typically halving the ion heat flux for a given ion temperature gradient length (Garcia et al. Reference Garcia, Görler and Jenko2018). The higher fast ion pressure in deuterium plasmas heated by energetic ions has led to improved core confinement in a set of L-mode experiments in JET, with ³He minority ion cyclotron resonance heating (ICRH) in addition to NBH (Bonanomi et al. Reference Bonanomi, Casiraghi, Mantica, Challis, Delabie, Fable, Gallar, Giroud, Lerche and Lomas2019b). It is important to stress that a different fast ion contribution in different plasma species is not an inherent isotope effect. In the case of a comparison of D and DT plasmas such an effect, if not understood, may lead to erroneously attributing the improved confinement in DT to a mass dependence.

Modelling of transport in the edge plasma and pedestal is still in its infancy, but deserves particular attention, as it sets the boundary conditions and via profile stiffness influences and often largely determines global confinement (Bateman et al. Reference Bateman, Kritz, Parail and Cordey1999). Strong ion mass effects have been obtained in electromagnetic gyrokinetic GENE simulations of L-mode edges in AUG and JET (Bonanomi et al. Reference Bonanomi, Angioni, Crandall, Di Siena, Maggi and Schneider2019b). The results show that edge turbulence is radically distinct from core turbulence. Electron parallel dynamics is important due to the high collisionalities at the edge, leading, in linear electrostatic simulations, to a stronger non-adiabatic electron response at low ion mass and to a lower R/L _Te threshold for hydrogen than for deuterium. This linear effect is also seen in nonlinear simulations, resulting in a strong deviation from gyroBohm $( {\chi _\textrm{H}}\sim 2{\chi _\textrm{D}}) $ already in electrostatic simulations. Due to the steep gradients, electromagnetic effects are also important despite the relatively low local thermal β. MHD-like electron drift waves are strongly destabilised even at low (with respect to core values) values of β_e. This destabilisation especially affects modes with low wave numbers and is found to take place below the threshold in β_e expected from linear simulations (Bonanomi et al. Reference Bonanomi, Angioni, Crandall, Di Siena, Maggi and Schneider2019b). This behaviour puts into question the applicability in the edge plasma of the conventional approach of developing quasilinear models for describing transport. These novel results on the L-mode edge call for an extension of gyrokinetic modelling to the H-mode pedestal, which is found to be responsible for most of the isotope scaling of confinement observed in JET H-modes, as reported in § 5.

2.2. Operational effects

It is difficult, and often impossible, to perform experiments in which an isotope is substituted for another, without changing any other plasma parameters. These operational effects can obscure the intrinsic transport effects, making their unambiguous identification difficult. Neutral beam heating and ICRH confer heat to electrons and ions in proportions which depend on the background ion as well as on the fast particle masses and energies. Moreover, no ICRH method can be applied indistinctly to plasmas with arbitrary isotopes or isotope mixtures. The power, torque and particle sources by NBH depend on both beam ion isotopes and hence also on the background plasma, as the general preference is to use the same species for NBH as for the main plasma. This warning can be extended to a comparison of D and DT plasmas, as the latter, unlike the former, will produce alpha particles which are potentially capable of reducing ITG turbulence by electromagnetic effects (Garcia, Görler & Jenko Reference Garcia, Görler and Jenko2018).

Equipartional energy exchange between ions and electrons, as well as between ions, depends on the plasma isotopes, affecting the ion and electron power balances and hence transport. Such a case was reported from a comparison of ECH heated L-mode in hydrogen and deuterium in ASDEX-upgrade (Schneider et al. Reference Schneider, Bustos, Hennequin, Ryter, Bernert, Cavedon, Dunne, Fischer, Görler and Happel2017). The two discharges achieved the same electron temperature profiles and nearly the same ion temperature profiles, although the hydrogen discharge required 1.4 MW of ECH power for only 1.06 MW for the deuterium discharge. A species resolved power balance calculation revealed that the electron heat flux was unchanged, however the ion heat flux was 1.5–2 times larger due to stronger electrons–ion thermal equipartition for the hydrogen case. The additional heat flux had virtually no effect in the ion temperature profile because of profiles stiffness as modelled using a critical gradient model (Garbet et al. Reference Garbet, Mantica, Ryter, Cordey, Imbeaux, Sozzi, Manini, Asp, Parail and Wolf2004). In JET ohmic discharges too, the difference in electron–ion equipartition between hydrogen and deuterium was found to be a key parameter in understanding the observed somewhat larger ion heat diffusivity in hydrogen (Delabie et al. Reference Delabie, Nave, Baruzzo, Bernardo, Boom, Buchanan, Hawkes, Hillesheim, Maggi and Menmuir2017).

The edge neutral penetration is deeper for the lighter species, which is expected to help fuelling for the lighter species. Cryopumping is more effective for the heavier hydrogenic species, affecting divertor and edge conditions. Orbit losses are reduced for the lighter species. Some effects are not understood, as for instance the cause of the much higher particle transport in the edge of hydrogen H-modes in JET-ILW (Maggi et al. Reference Maggi, Weisen, Hillesheim, Chankin, Delabie, Horvath, Auriemma, Carvalho, Corrigan and Flanagan2018) and ASDEX-upgrade (Laggner et al. Reference Laggner, Wolfrum, Cavedon, Mink, Bernert, Dunne, Schneider, Kappatou, Birkenmeier and Fischer2017) (but not in JT-60U Urano et al. (Reference Urano, Takizuka, Aiba, Kikuchi, Nakano, Fujita, Oyama, Kamada and Hayashi2013)), which affect overall confinement. The planned DT experiments in JET have prompted a multi-campaign investigation of isotope effects in view of understanding the physics and in order to provide better extrapolation to the performance to be expected from the discharges under preparation for DT. Many of the results in hydrogen and deuterium plasmas have already been reported and will not be repeated here (Maggi et al. Reference Maggi, Weisen, Hillesheim, Chankin, Delabie, Horvath, Auriemma, Carvalho, Corrigan and Flanagan2018, Reference Maggi, Weisen, Casson, Auriemma, Lorenzini, Nordman, Delabie, Eriksson, Flanagan and Keeling2019).

5.1. Global thermal confinement in type I ELMy H-mode

The thermal stored energy is calculated as in (4.1). Unlike the case for L-modes, the electron density in deuterium H-modes is essentially uncontrollable using gas puffing (Maggi et al. Reference Maggi, Saarelma, Casson, Challis, de la Luna, Frassinetti, Giroud, Joffrin, Simpson and Beurskens2015; Urano et al. Reference Urano, Hobirk, Maggi and Joffrin2016; Maslov et al. Reference Maslov, Boboc, Brix, Flanagan, Peluso, Price and Romanelli2020). We therefore here avoid $\langle {n_e}\rangle $ as a regression parameter. Regressions including the density have been presented in Maggi et al. (Reference Maggi, Weisen, Hillesheim, Chankin, Delabie, Horvath, Auriemma, Carvalho, Corrigan and Flanagan2018), Weisen et al. (Reference Weisen, Maggi, Menmuir, Horvath, Bache, Casson, Oberparleiter, Saarelma, Auriemma and Chankin2018), with similar results for the ion mass scaling. Instead, we use the Balmer-α radiation along a horizontal line as a proxy for edge fuelling. The intensity of Balmer-α emission scales with the gas puff rate roughly within a factor 2, over a factor of 20 variation in the dataset, however, better regressions are obtained with the Balmer-α emission than with the gas puff rate. Satisfactory regressions using the divertor Balmer-α radiation or the gas puff rate are also obtained, however, the Balmer-α radiation along a horizontal line provides the regressions with the lowest standard deviation.

The regression for W _th is shown in figure 7 and given below:

(5.1)\begin{equation}{W_{\textrm{th}}}\propto {\boldsymbol{A}^{\boldsymbol{0}.\boldsymbol{53} \pm 0.05}}{P^{0.63 \pm 0.04}}I_p^{0.83 \pm 0.08}{\varGamma ^{ - 0.17 \pm 0.04}}.\end{equation}

Figure 7.

Regression of the thermal confinement time in MJ correponding to (5.1). P _tot is the total power, A is the isotope mass, $\langle {n_e}\rangle $ is the volume average density and σ the standard deviation. The legend is explained in the main text in § 4.

The standard deviation of this regression is 0.09. A very similar result is obtained if we regress for the thermal energy inferred from W _MHD as in (4.1)

(5.2)\begin{equation}{W_{\textrm{th}}}\propto {\boldsymbol{A}^{\boldsymbol{0}.\boldsymbol{48} \pm 0.05}}{P^{0.67 \pm 0.04}}I_p^{0.86 \pm 0.09}{\varGamma ^{ - 0.2 \pm 0.03}}, \end{equation}

with a standard deviation of 0.094. (Regression in (5.2) is too similar to (5.1) to deserve its own figure.)

These scalings have a slightly stronger isotope dependence than reported in Maggi et al. (Reference Maggi, Weisen, Hillesheim, Chankin, Delabie, Horvath, Auriemma, Carvalho, Corrigan and Flanagan2018), which found ${W_{\textrm{th}}}\propto {A^{0.4}}$ using the plasma density rather than a measure of gas fuelling and assuming T_i = T_e. The scaling is significantly stronger scaling than in JET-C (JET Team 1999; Saibene et al. Reference Saibene, Horton, Sartori, Balet, Clement, Conway, Cordey, De Esch, Ingesson and Lingertat1999) and in the IPB(y,2) ELMy H-mode scaling $( {W_{\textrm{th}}}\propto {A^{0.19}}) $ (ITER Physics Basis 1999). A recent broad survey of H-mode confinement in JET, with 867 JET-ILW samples, including deuterium (the majority) and hydrogen plasmas also reports a strong isotope scaling in JET-ILW, with mass exponents in the range 0.35 to 0.43, depending on the choice of regression variables and data subsets (Maslov et al. Reference Maslov, Boboc, Brix, Flanagan, Peluso, Price and Romanelli2020). In that study, the thermal stored energy was inferred from the diamagnetic energy which is based on external magnetic measurements, corrected for the perpendicular fast ion energy content. Interestingly, that study also finds that the mass exponents are somewhat higher when a measure of gas fuelling is used instead of the plasma density. Altogether, this paper and Maggi et al. (Reference Maggi, Weisen, Hillesheim, Chankin, Delabie, Horvath, Auriemma, Carvalho, Corrigan and Flanagan2018), Maslov et al. (Reference Maslov, Boboc, Brix, Flanagan, Peluso, Price and Romanelli2020), show that isotope scaling of thermal energy confinement in JET-ILW is robust to the choice of data sets and regression variables.

The normalised hydrogen and deuterium temperatures are similar, regardless of conditions. In figure 8 we show ∇T_e as function of T_e for ρ _pol = 0.8 and 0.55. As the HRTS system suffered a miscalibration at 3 channels near the pedestal top for part of the data, we show these using data from the LIDAR Thomson scattering system. There is no discernible systematic difference in ∇T_e/T_e between the two species, nor for the different heat fluxes, which span a factor 9 at ρ = 0.55 (figure 8a). In the meaning of stiffness as defined in Garbet et al. (Reference Garbet, Mantica, Ryter, Cordey, Imbeaux, Sozzi, Manini, Asp, Parail and Wolf2004), we see no evidence for a difference in stiffness between the two species, as already stated in Maggi et al. (Reference Maggi, Weisen, Hillesheim, Chankin, Delabie, Horvath, Auriemma, Carvalho, Corrigan and Flanagan2018).

Figure 8.

∇T_e as function of T_e for (a) ρ _pol = 0.55 and (b) ρ _pol = 0.8. The dashed lines correspond to the averages of R ∇T_e/T_e.

When normalised to the gyroBohm heat flux defined as ${Q_{\textrm{gB}}} = {( A{m_p}) ^{0.5}}{n_e}{( e{T_i}) ^{2.5}}R/ {L_{\textrm{Ti}}}/( {e^2}{B^2}R_{\textrm{geo}}^2) {R_{\textrm{geo}}}/{L_{\textrm{ref}\,f}}[ \textrm{W}\,{\textrm{m}^{ - 2}}] $ (Garbet et al. Reference Garbet, Mantica, Ryter, Cordey, Imbeaux, Sozzi, Manini, Asp, Parail and Wolf2004), the range of ion heat fluxes in the dataset is even larger, as seen in figure 9 for ρ = 0.6 as function of R/L _Ti. For this calculation we adopted L _ref = R _geo as the reference scale length, assumed the effective surface for the calculation of the heat flux to be S _eff = dV/dr, with V the plasma volume, r = (R _max − R _min)/2 and R _geo = (R _max − R _min)/2, R _max and R _min being the maxima and minima of the flux surfaces at the plasma mid-plane. Although errors on the normalised heat flux and on R/L _Ti are large, we see that the measured gradients are mostly in the range 5 < R/L _Ti < 8 for both isotopes over a range of normalised heat fluxes, Q_i/Q _gB, of a factor 20. No dependence of Q_i/Q _gB on R/L _Ti, nor on the isotope is discernible. A possible species dependence, as reported in Urano et al. (Reference Urano, Takizuka, Aiba, Kikuchi, Nakano, Fujita, Oyama, Kamada and Hayashi2013), is likely to be obscured by a combination of experimental errors and of unresolved dependences of the critical gradient R/L _crit (Garbet et al. Reference Garbet, Mantica, Ryter, Cordey, Imbeaux, Sozzi, Manini, Asp, Parail and Wolf2004) on the wide range of plasma conditions in the dataset.

Figure 9.

Ion heat flux in gyroBohm units vs normalised ion temperature gradient at ρ = 0.6.

The density profiles of hydrogen and deuterium plasmas are remarkably similar too. The volume average density can be regressed as $\langle {n_e}\rangle = 0.92{n_e}( 0.9) + 0.35 \times {10^{19}}\,{\textrm{m}^{ - 3}}$ for both species, as seen in figure 10. (This implies that plasmas with lower density have somewhat more peaked density profiles.) Together with the similarity of temperature profiles, this implies that the global electron energy is proportional to the electron energy at ρ _pol = 0.9, which we take as a proxy of the pedestal electron energy (figure 11). The ratios of the pedestal to global stored electron energies for both species are well within error bars, ${W_{\textrm{pede}}}/{W_{\textrm{th}}} \approx 0.56$ in deuterium and ${W_{\textrm{pede}}}/{W_{\textrm{th}}} \approx 0.54$ in hydrogen. Hence, to within measurement errors, the species related differences in electron stored energy are attributable to differences in the pedestal. Ion temperatures are less stiff as T_i/T_e increases with $P/\langle {n_e}\rangle $ more strongly in the core than nearer the pedestal top. Assuming T _ieq(f_i = 0.2, ρ)/T_e(ρ), this increase would be stronger for deuterium than for hydrogen as seen in figure 6(c), contributing, albeit very modestly, to better global confinement in deuterium. Unfortunately, accurate core ion temperature measurements, not available at this time, are required for backing up this conjecture.

Figure 10.

Scaling of average density with pedestal density.

Figure 11.

Proportionality of global and pedestal stored energies.

5.2. Momentum confinement in type I ELMy H-mode

Fortunately, the errors on angular velocity determined from CXS are lower than those on T_i and measurements are available for about half of the H-mode dataset. The maximum torque in the dataset was 20 Nm in deuterium and 12 Nm in hydrogen at the maximum NBH powers available. The global momentum ranged up to 4.7 Nms in deuterium and 1.8 Nms in hydrogen. Global angular momentum in hydrogen plasmas is considerably lower than in deuterium plasmas due to the lower NBH torque, the lower density and confinement.

The total momentum L was obtained by volume integration of the local toroidal momentum density $l = {\omega _\phi }{\rho _m}{R^2}$, where ω_ϕ is the toroidal angular velocity from CXS, ρ_m the plasma mass density and R the distance from the torus axis. Figure 12 shows that the global momentum confinement time τ_ϕ = L/T, where T is the NBH torque calculated by PENCIL (Challis et al. Reference Challis, Cordey, Hamnen, Stubberfield, Christiansen, Lazzaro, Muir, Stork and Thompson1989), can range between 0.6 and 1.3 times the thermal energy confinement time, consistently with earlier observations which show χ_ϕ ~ 0.8 χ_i (Weisen et al. Reference Weisen, Camenen, Salmi, Versloot, Devries, Maslov, Tala, Beurskens and Giroud2012). A close relationship between the isotope scaling of energy and momentum confinement has already been observed in ASDEX (Bessenrodt-Weberpals et al. Reference Bessenrodt-Weberpals and Wagner1993). The highest ratios τ_ϕ/τ_E are obtained at the lowest ELM frequencies. As ELM frequencies correlate with gas puff rates and densities, the highest ratios τ_ϕ/τ_E also correspond to the lowest gas puff rates and the highest densities.

Figure 12.

Angular momentum confinement time vs thermal energy confinement time. The symbols refer to ELM frequencies. Hydrogen plasmas are marked with an additional red circle. The broken lines corespond to τ_ϕ/τ_E = 0.6 and 1.3, respectively.

Momentum confinement is very similar to the global energy confinement (see (5.1)), as seen in figure 13, where the total momentum was regressed as

(5.3)\begin{equation}L \propto {\boldsymbol{A}^{\boldsymbol{0}.\boldsymbol{56} \pm 0.12}}{T^{0.43 \pm 0.09}}I_p^{1.1 \pm 0.21}{\varGamma ^{ - 0.4 \pm 0.08}}.\end{equation}

Figure 13.

Regression for global angular momentum L in Nms in ELMy H-modes correponding to (5.3).

This is significant as momentum is not transported by electrons, showing that the electrons cannot be responsible for the majority of heat transport in these discharges. The dominance of ion transport in JET discharges has also been documented in a comprehensive study of the interspecies power balance in JET (Weisen et al. Reference Weisen, Delabie, Flanagan, Giroud, Maslov, Menmuir, Patel, Scott, Siren and Varje2020) and is consistent with the ITG regime being the dominant transport regime in most JET plasmas with dominant NBH. The negative dependency on Γ of L_ϕ in (5.3) is stronger than that of W _th in (5.1). It is not clear whether this is a result of ELM losses, which may have an electromagnetic component not shared with the thermal plasma, or a result of charge exchange losses.

5.3. Particle confinement in type I ELMy H-modes

The particle content can be regressed as

(5.4)\begin{equation}{N_e}\propto {\boldsymbol{A}^{\boldsymbol{0}.\boldsymbol{57} \pm 0.05}}{\varGamma ^{0.24 \pm 0.03}}f_{\textrm{ELM}}^{ - 0.12 \pm 0.03}, \end{equation}

where f _ELM is the ELM frequency and Γ the Balmer-α emission from the divertor, measured using arrays vertically viewing both the inner and the outer divertor (figure 14).

Figure 14.

Regression for the total electron content according to (5.4). Dadiv stands for divertor Balmer-α emission and felm for the ELM frequency.

The isotope mass is the most important contributor to this scaling (STR = 0.66), well ahead of the ELM frequency (STR = 0.28), showing that the differences in ELM frequency are not the only cause (and most likely not the main cause) for the lower density in hydrogen type I ELMy H-modes at low triangularity, as in these experiments. Remarkably, neither the heating power, nor the plasma current appear to have an impact on particle confinement, despite the proximity of a fraction of the cases to the Greenwald density limit (Greenwald et al. Reference Greenwald, Terry, Wolfe, Ejima, Bell, Kaye and Neilson1988). There is also no significant correlation between I_p and Γ.

The isotope dependence of particle confinement is similar to that for energy and momentum and suggest that the poor energy and momentum confinement in hydrogen H-modes may be due to the low particle confinement, in particular in the pedestal. Lower pedestal densities in hydrogen, combined with similar, stiff temperature profiles would lead to lower energy confinement. However, such a narrative would not fit JT-60U results, from which no such difference in particle confinement is reported (Urano et al. Reference Urano, Takizuka, Aiba, Kikuchi, Nakano, Fujita, Oyama, Kamada and Hayashi2013), but instead, a difference in temperatures. At present the difference with JT-60U is not understood, and we limit our comparison to pointing out a few of the differences between the two devices, including the usage of carbon plasma facing components (PFCs) in JT60-U, a substantially larger toroidal field ripple in JT60-U leading to fast ion losses, which induce a torque directed counter to I_p, the usage of near perpendicularly injected low torque NBH for hydrogen, reinforcing fast ion losses. The JT-60U hydrogen plasmas were slowly counter-rotating $( {\omega _\phi }\sim{-} {10^4}\;\textrm{rad}\,{\textrm{s}^{ - 1}}) $, while the deuterium plasmas were slowly co-rotating $( {\omega _\phi }\sim + 10^4\;\textrm{rad}\,{\textrm{s}^{ - 1}}) $ (Urano et al. Reference Urano, Takizuka, Aiba, Kikuchi, Nakano, Fujita, Oyama, Kamada and Hayashi2013). JET ELMy H-modes plasmas with comparable NBH power co-rotated at much higher frequencies, ω_ϕ ranging from 3 to 7 × 10⁴ rad s⁻¹.

Here, our liberal use of the Balmer-α emission as a proxy for the particle source deserves a discussion. This method is based on the approximate proportionality of Balmer-α photon emission rates and hydrogen isotope ionisation rates (Johnson & Hinnov Reference Johnson and Hinnov1973). We find that in the above regressions, this emission leads to narrower fits than the usage of the gas injection rate into the vessel and therefore accept them as better proxies for the particle flux into the plasma. It is however not clear why, for some cases, the main chamber Balmer-α emission provides narrower regressions than the divertor radiation or vice versa. Strictly speaking, the edge source should only be inferred from Balmer-α emission from inside the last closed flux surface (LCFS). In practice this is close to impossible, except if tomographically inverted Balmer-α emission data from a tangentially viewing visible camera equipped with an interference filter are available, which was not the case for this study. Hence the light collected along single vertical or horizontal viewing lines will contain both emission from inside and outside the LCFS. The uncertainties concerning the spatial origin of this light are further acerbated by reflections at the metallic vessel walls. Divertor emission in the dataset is two orders of magnitude larger than main chamber emission, hence most of the light collected by divertor views originates from outside the LCFS. We therefore interpret divertor Balmer-α light as a likely proxy for the neutral density outside the LCFS, which is also proportional to the particle flux into the plasma.

5.4. Transport in mixed isotope ELMy H-modes

Experiments at I_p = 1.4 MA and B _T = 1.7 T with 8–10 MW of NBH in mixed hydrogen/deuterium plasmas have allowed to scan the effective mass ${A_{\textrm{eff}}} = {\sum _i}{A_i}{n_i}/{\sum _i}{n_i}$ (for i = 1, 2) from 1 to 2 (King et al. Reference King, Viezzer, Baruzzo, Belonohy, Buchanan, Carvalho, Cave-Ayland, Coffey, Challis and Delabie2017, Reference King, Viezzer, Balboa, Baruzzo, Belonohy, Buchanan, Carvalho, Cave-Ayland, Coffey and Challis2020). The isotope composition was inferred from the line intensity ratios of the Balmer-α lines of the two species, as measured from high resolution divertor spectroscopy (Neverov et al. Reference Neverov, Kukushkin, Stamp, Alekseev, Brezinsek and von Hellermann2017). Below 10 MW, in pure hydrogen, a type I ELMy regime was not always achieved. Instead, these plasmas had type III ELMs and W _th ~ 0.8 MW. The pure hydrogen point, as well as the deuterium one, were taken from equivalent plasmas in the dataset presented in §§ 5.2–5.4. The thermal stored energy in these discharges does not rise linearly with A _eff, instead exhibiting a plateau with near constant stored energy for 1.2 ≤ A _eff ≤ 1.8, seen in figure 15 for 8 ≤ P _NBH ≤ 10 MW (King et al. Reference King, Viezzer, Balboa, Baruzzo, Belonohy, Buchanan, Carvalho, Cave-Ayland, Coffey and Challis2020). While the plateau stored energy is constant, however, the pedestal density rises from near 2.3 × 10¹⁹ m⁻³ for A _eff < 1.5 to ~3 × 10¹⁹ m⁻³ for A _eff = 1.85, while at the same time the pedestal temperature drops from ~0.6 keV to 0.5 keV (King et al. Reference King, Viezzer, Balboa, Baruzzo, Belonohy, Buchanan, Carvalho, Cave-Ayland, Coffey and Challis2020). The beam species for the mixed plasmas were also mixed, but consisted mostly of hydrogen and where therefore not matched to the bulk plasma composition established by adjusting the gas puff rates for the two species. This mismatch had no incidence of the confinement time, as shown by a comparison of pure hydrogen and pure deuterium injection at the same power into otherwise identical discharges.

Figure 15.

Thermal stored energy in isotope ratio scan at fixed current and power for H-mode plasmas with type I ELMS. The data points in red are from pure hydrogen and deuterium experiments. From King et al. (Reference King, Viezzer, Balboa, Baruzzo, Belonohy, Buchanan, Carvalho, Cave-Ayland, Coffey and Challis2020).

The plateau is reminiscent of a very similar plateau in L–H threshold power P _L-H observed in a different experiment (Hillesheim et al. Reference Hillesheim, Delabie, Solano, Maggi, Meyer, Belonohy, Carvalho, de la Luna, Drenik and Gelfusa2018). This similarity may be linked to general observation that the confinement enhancement factor over IPB98 scaling (ITER Physics Basis 1999) H-modes improves with P/P _L-H. These experiments were not repeated to establish the P _L-H threshold power, but from similar experiments (Hillesheim et al. Reference Hillesheim, Delabie, Solano, Carvalho, Drenik, Giroud, Huber, Lerche, Lomanowski and Mantsinen2017) we estimate that in pure hydrogen plasmas P _L-H was barely exceeded, while for pure D it was higher than 2.

In several of the H-mode experiments deuterium NBH was used with a hydrogen background plasma. The core isotope composition was inferred from the measured neutron rates, showing that it only modestly exceeded the one measured using divertor Balmer-α spectroscopy (Maslov et al. Reference Maslov, King, Viezzer, Keeling, Giroud, Tala, Salmi, Marin, Citrin and Bourdelle2018). As a result the shape of both ion isotope profiles remained close to that of the electrons. Transport simulations and quasilinear gyrokinetic modelling of the isotope profiles in these experiments have shown that the ion particle diffusion coefficient D_i can be as high as 2χ _eff in the ITG mode, which, combined with strong inward convection leads to fast isotope mixing throughout the plasma cross-section (Bourdelle et al. Reference Bourdelle, Bourdelle, Camenen, Citrin, Marin, Casson, Koechl and Maslov2018; Maslov et al. Reference Maslov, King, Viezzer, Keeling, Giroud, Tala, Salmi, Marin, Citrin and Bourdelle2018; Marin et al. Reference Marin, Citrin, Bourdelle, Camenen, Casson, Ho, Koechl and Maslov2020). This is in stark contrast with the electron particle transport, which governs the electron density profile and is characterised by transport coefficients an order of magnitude smaller than those for the ions. In TEM mode (not the case in these experiments), the ion transport coefficients from gyrokinetic modelling would be much smaller and isotope mixing is expected to be considerably slower (Bourdelle et al. Reference Bourdelle, Bourdelle, Camenen, Citrin, Marin, Casson, Koechl and Maslov2018) as observed in LHD (Ida et al. Reference Ida, Nakata, Tanaka, Yoshinuma, Fujiwara, Sakamoto, Motojima, Masuzaki, Kobayashi and Yamasaki2020). Core isotope ratio control has also been demonstrated by shallow (low penetration) deuterium pellets injected into a plasma simultaneously fuelled by hydrogen gas and hydrogen NBH (Valovic et al. Reference Valovic, Baranov, Boboc, Buchanan, Citrin, Delabie, Frassinetti, Fontdecaba, Garzotti and Giroud2019). A core H/D ratio n _H/n _D ≈ 1.2, close to the target of n _H/n _D = 1, was obtained despite the different fuelling methods for the two species, as inferred from core hydrogen isotope CXS and from the neutron rates. Fast mixing greatly eases isotope ratio control, as it matters little (in ITG mode) how and where the main ion species are introduced into the plasma, boding well for isotope ratio control in the upcoming JET D-T experiments and in ITER.

5.5. Particle transport in the H-mode pedestal

Since core temperature profiles are essentially stiff (large variations in the heat flux only lead to small variations of R/L_T = R ∇T/T), pedestal conditions are the main contributors to the isotope effect manifested throughout the plasma in these JET-ILW experiments. The pedestal structure, MHD stability and ELM behaviour in hydrogen and deuterium ELMy H-modes have been extensively documented (Horvath Reference Horvath2019; Horvath et al. Reference Horvath, Maggi, Chankin, Saarelma, Field, Aleiferis, Belonohy, Boboc, Corrigan and Delabie2020). We here only summarise finding of direct relevance to the observed reduced particle confinement in hydrogen plasmas. At low ELM frequencies (f _ELM < 40 Hz) ELM particle losses increase with ELM frequency, correlating with lower pedestal top densities and showing that the increased ELM frequencies may contribute to lower hydrogen edge densities. Pedestal top densities in both species are similar at similar ELM frequencies. However there is not a unique relationship between the particle loss rate attributable to the ELMs (f _ELM ΔN _ELM, where ΔN _ELM is the number of particles lost per ELM) and the pedestal density, suggesting that other mechanisms, such as particle transport other than by ELMs also play a role (Horvath Reference Horvath2019, PhD thesis; Horvath et al. Reference Horvath, Maggi, Chankin, Saarelma, Field, Aleiferis, Belonohy, Boboc, Corrigan and Delabie2020, sub. NF). This observation is consistent with the regression (5.4), which identifies the ELMs as a significant, but not the main, player in determining the plasma particle content.

The necessity for stronger fuelling in hydrogen is at odds with popular conceptions of fuelling by neutral penetration, as for all other parameters being equal (e.g. T_i), hydrogen neutrals should penetrate deeper into the plasma, thanks to their greater thermal velocity. The observation suggests that transport processes in the pedestal may overcome the effect of thermal velocity. The pedestal width model (Groebner et al. Reference Groebner, Mahdavi, Leonard and Osborne2002) based on neutral penetration is inconsistent with observations of hydrogen and deuterium pedestals. This model predicts a pedestal width scaling as $\;{\Delta _{\textrm{ne}}}\propto {v_n}r_i^{ - 1}n_{e\,\textrm{ped}}^{ - 1}\propto {A^{ - 1/2}}n_{e\,\textrm{ped}}^{ - 1}$, where $v_n$ is the neutral velocity and r_i the ionisation rate, which is temperature dependent. At 1.4 MA/1.7 T there is no clear dependence of Δ_ne on species, nor on ${n_{e\,\textrm{ped}}}$. In the 1 MA/1 T subset the measured widths, taken shortly before the ELM crashes, deviate by a factor two from the scaling (see e.g. figure 11 in Weisen et al. Reference Weisen, Maggi, Menmuir, Horvath, Bache, Casson, Oberparleiter, Saarelma, Auriemma and Chankin2018). This remains the case even when the effects of the temperature dependent neutral velocity and ionisation rates are taken into account (Horvath Reference Horvath2019, PhD thesis; Horvath et al. Reference Horvath, Maggi, Chankin, Saarelma, Field, Aleiferis, Belonohy, Boboc, Corrigan and Delabie2020). This shows that the pedestal density width cannot be inferred from neutral penetration alone. We conclude that transport processes, still poorly understood, also contribute to shaping the pedestal.

EDGE2D EIRENE (Simonini et al. Reference Simonini, Corrigan, Radford, Spence and Taroni1994; Wiesen Reference Wiesen2006) was used to model the plasma boundary and pedestal region of a pair of H-modes in the two species. Both species required a transport barrier to model the pedestal and near SOL of 3 cm width. In hydrogen the required particle diffusion coefficient was as much as 5 times higher than in deuterium. When only the isotope was changed to hydrogen in a simulation for deuterium, there was only a modest change in T_e and n_e profiles, which was opposite in sign to the observations. The analysis shows that plasma density profiles in the boundary are governed also by particle transport processes and are more complex than expected from neutral fuelling physics only. We expect better insights into the nature of transport in the H-mode pedestal and its dependence on the isotope species from gyrokinetic modelling (like the one in Bonanomi et al. Reference Bonanomi, Angioni, Crandall, Di Siena, Maggi and Schneider2019b, for the L-mode edge) in conjunction with the application of MHD stability constraints.

5.6. Nonlinear gyrokinetic modelling of core heat transport in hydrogen and deuterium type I ELMy H-modes

A pair of hydrogen and deuterium discharges with same heating power (10 MW) from the type I ELMy H-mode dataset, has been analysed with flux-tube simulations at ρ = 0.5 using the gyrokinetic code GENE (Jenko et al. Reference Jenko, Dorland, Kotschenreuther and Rogers2000; Görler et al. Reference Görler, Lapillonne, Brunner, Dannert, Jenko, Merz and Told2011) and assuming T_i = T_e. The hydrogen plasma had a lower volume average density, electron temperature and thermal stored energy ($\langle {n_e}\rangle = 2.1 \times {10^{19}}\;{\textrm{m}^{ - 3}}$, ${T_e}( 0) = 2.9\;\textrm{keV}, \;\;{W_{\textrm{th}}} = 1.25\;\textrm{MJ}$) than the deuterium plasma ($\langle {n_e}\rangle = 2.8 \times {10^{19}}\;{\textrm{m}^{ - 3}}$,${T_e}( 0) = 3.9\;\textrm{keV}, \;\;{W_{\textrm{th}}} = 2.34\;\textrm{MJ}$). Linear simulations including the effect of collisions show no significant deviations from Gyro-Bohm scaling. Nonlinear electromagnetic simulations including the effect of collisions using the standard drift-kinetic Landau–Boltzmann collision operator, E × B shear from the sheared rotation measured by CXS and dilution by Be impurities using the experimental temperature gradients lead to an over-prediction of the measured heat fluxes by a factor 2 for hydrogen and a factor 6 for deuterium, as seen in figure 16.

Figure 16.

Scan of mid-radius heat flux versus normalised gradient $a/{L_{\textrm{Te}}} ={-} a{\bf \nabla }{T_e}/{T_e}$ calculated by GENE versus temperature gradient, assuming T_i = T_e. Orange: hydrogen, blue: deuterium. The experimental points are shown as a diamond (hydrogen) and a dot (deuterium).

Figure 16 shows the result of a scan of normalised temperature gradient $a/{L_{\textrm{Te}}} = a{\bf \nabla }{T_e}/{T_e}$ at ρ_t = 0.5, where a is the minor radius, performed in order to find a match for the experimental heat flux. They show that the simulated heat fluxes can be approximately matched by reducing the temperature gradients by 20 % in the hydrogen discharge and by 17 % in deuterium. The simulations also show that deuterium transport is stiffer than the hydrogen one, but has the advantage of a higher instability threshold. At the modest heat flux in the experiment, Q _tot ≈ 70 kW m⁻³, below the crossing point where Q _tot is the same for both isotopes, this allows for steeper gradients and hence larger temperatures in the deuterium case.

Figure 17 shows the results from a range of nonlinear flux-tube GENE calculations at mid-radius undertaken to clarify the importance of collisions, E × B shear and dilution by Be impurities. For these calculations the gradients were adjusted, as indicated above, such as to obtain heat fluxes matching those of the experiment (black bars in figure 17). For each discharge, simulations were performed assuming A = 1 and A = 2. In the absence of collisions, the simulated heat fluxes exceed the experimental ones by factors of 4–15 (green bars in figure 17). Collisions are essential for obtaining realistic heat fluxes, as seen when comparing the simulations without collisions (green bars) with those where E × B from sheared toroidal rotation (red) or impurities (orange) were left out. Collisions are seen to enhance the zonal flow shearing rate ω_E × B spectra, reducing ITG amplitudes and suppressing TEM modes. Leaving out E × B from sheared toroidal rotation has little effect, except for the simulation of the D discharge wit A = 2 (figure 17b). However the reduction by E × B stabilisation is always larger when A = 2 is chosen in the simulations, than when A = 1 is chosen, consistently with the qualitative sketch in figure 1. Neglecting Be impurities also leads to ~30 % higher heat fluxes (figure 16a), mainly as a result of dilution of the main species.

Figure 17.

Summary of nonlinear GENE simulations in hydrogen and deuterium ELMy H-modes. Both discharges were simulated assuming A = 1 and A = 2. Black bars: experimental heat flux (same in (a) and (b)), blue bars: complete simulation with all effects. Other bars: simulations with one or more effects left out. The bars in violet are for a case when both collisions and E × B shear from bulk toroidal rotation are excluded. The divisions of the bars into parts with different shading indicate, from bottom to top, the ion, electron and Be contributions to the total heat flux.

The effect of collisions is to cause a narrowing of the spectra of heat and particle fluxes by a factor 2 for hydrogen and a factor 3–4 for deuterium, as seen in figure 18. The figure shows the spectral heat and particle fluxes for 4 simulations based on the hydrogen experimental case, with (figure 18a,b) and without (figure 18c,d) collisions assuming A = 1 (figure 18a,c) and A = 2 (figure 18b,d). ${k_y}{\rho _{\textrm{sH}}}$ is the poloidal wavenumber normalised with the ion Larmor radius calculated for hydrogen. The figure shows both the electrostatic heat and particle fluxes (noted Q _es and Γ _es) and the magnetic flutter components (Q _em and Γ _em), which are comparatively small. In the absence of collisions, the peak amplitudes of the fluxes are higher for deuterium, although the spectral widths are somewhat smaller. The flux spectra are strongly affected by the collisions, becoming narrower and shifted to higher poloidal wavenumbers: $\langle {k_y}{\rho _{\textrm{sH}}}\rangle \sim 0.42$ and ~0.36 with collisions for A = 1 and 2 respectively and $\langle {k_y}{\rho _{\textrm{sH}}}\rangle \sim 0.3$ and ~0.22 without collisions. Spectral amplitudes are only slightly reduced in the presence of collisions, hence the narrower spectra in deuterium are the main cause for the smaller fluxes. This spectral narrowing is due to electron-ion collisions suppressing TEM modes virtually completely. The stark differences between the cases in figure 18 are well apparent in the cross-phase angle α between potential fluctuations and density fluctuations seen in figure 19. The figure shows the probability distribution functions (PDFs) for the cross-phase angle α as function of α and ${k_y}{\rho _{\textrm{sH}}}$, weighted as described in Dannert & Jenko (Reference Dannert and Jenko2005). Outward particle transport occurs essentially for the positive angles in the region ${k_y}{\rho _{\textrm{sH}}} \lt 0.6$. The region ${k_y}{\rho _{\textrm{sH}}} \gt 0.6$ in figure 19(c,d) (no collisions, no E × B shear) with finite PDF around $\alpha ={\pm} {\rm \pi} $ is due to TEMs and is absent in the collisional cases with E × B shear (subplots a and b).

Figure 18.

Spectral heat and particle fluxes with collisions and rotational E × B shear (a and b) and without collisions nor E × B shear (c and d), assuming A = 1 (a,c) and A = 2 (b,d).

Figure 19.

Probability distributions for the cross-angle between potential and density fluctuations for simulations with collisions and rotational E × B shear (a,b) and without collisions nor E × B shear (c,d), assuming A = 1 (a,c) and A = 2 (b,d).

The resulting rms average of the zonal flow E × B shear rate is only ~10 % larger in deuterium than in hydrogen in the fully collisional case, but ~1.55 times larger in deuterium when normalised to the respective thermal velocities. This suggests that the main contributor to the larger zonal flow E × B shear stabilisation in deuterium is the isotope effect discussed in the introduction ((2.2) and figure 1). The results are little changed when ion-ion collisions are left out of the calculations. With only electron-ion collisions, fluxes are reduced to a level within 15 % of the full collisional case. This indicates that the reduced fluxes are primarily due to TEM suppression by electron-ion collisions.

These local nonlinear GENE simulations at mid-radius show that a reversal of gyroBohm scaling is consistent with the experimental observations. This is highly encouraging, but we should keep in mind that we cannot extrapolate to global scaling from any local core transport model alone. It is very likely that in global nonlinear simulations with experimentally imposed boundary conditions, e.g. at the top of the pedestal, the global confinement will be strongly dependent on the boundary conditions as a result of profile stiffness, i.e. the root cause for the lower transport in deuterium in these plasmas is still to be sought in the pedestal. A different pedestal boundary condition (higher or lower pedestal temperature for the same heat flux) would lead to different core conditions (higher or lower core temperature for the same heat flux).