Cross-machine comparison of runaway electron generation during tokamak start-up for extrapolation to ITER

A tokamak plasma may be considered non-thermal but this does not mean it necessarily contains a significant number of RE, merely that the electron energy distribution is non-Maxwellian. The so-called streaming parameter, ξ, can be used to indicate how non-thermal a tokamak plasma is, being the ratio of the velocity needed to carry the current, u_e, to the electron thermal velocity, v_eTH,

$$\begin{equation}\xi \equiv \frac{{{u_{\text{e}}}}}{{v_{\text{eTH}}}} = \frac{j}{{e{n_{\text{e}}}}}\frac{1}{{{v_{{\text{eTH}}}}}} = \frac{j}{{e{n_{\text{e}}}}}\sqrt {\frac{{{m_{\text{e}}}}}{{{k_{\text{B}}}{T_{\text{e}}}}}} .\end{equation} \tag{ 1 }$$

Here, n_e, T_e, e and k_B, are the electron density, temperature, electron charge and Boltzmann's constant, respectively, while j is the total current density. It is interesting to consider that an early Townsend discharge, which initiates most tokamak discharges, cannot be considered thermal [1]. But thereafter most tokamak plasmas thermalize, yielding a ξ < 0.1. While strongly non-thermal plasmas are those with ξ > 0.2 [2]. Having, a large streaming factor, and thus a non-Maxwellian electron energy distribution, does not mean RE can exist. RE are those electrons for which the Coulomb collisional drag by the fully ionized plasma is less than the acceleration these particles may feel from any electric field, E. One can show that electrons can freely accelerate, and thus can become REs, RE, if this electric field exceeds a critical electric field, E_c [2, 3, 7],

$$\begin{equation}{E_{\text{c}}} = \frac{{{n_{\text{e}}}{\text{ }}{e^3}{\text{ln }}\Lambda }}{{4\pi \varepsilon _{\text{o}}^2{m_{\text{e}}}{c^2}}} = 7.66\cdot{10^{ - 22}}{n_{\text{e}}}.\end{equation} \tag{ 2 }$$

Here, m_e is the electron mass and c is the speed of light. For simplicity, the Coulomb logarithm lnΛ is here assumed to be 15 [8]. The critical electric field can be compared with the so-called Dreicer electric field, E_D [9], which is the electric field for which the critical velocity for electrons to become RE is of the same order as the electron thermal velocity, thus determined by the temperature, T_e (eV), as:

$$\begin{equation}{E_{\text{D}}} = {E_{\text{c}}}\frac{{{m_{\text{e}}}{c^2}}}{{{k_{\text{B}}}{T_{\text{e}}}}} = \frac{{{n_{\text{e}}}{} {e^3}{} {{{{\text{ln }}\Lambda}}}}}{{4\pi \varepsilon _{\text{o}}^2{} {k_{\text{B}}}{T_{\text{e}}}}} = 3.9 \cdot {10^{- 16}}\frac{{{n_{\text{e}}}}}{{{T_{\text{e}}}\left( {{\text{eV}}} \right)}}.\end{equation} \tag{ 3 }$$

E_D is significantly larger than the critical electric field E_c because for tokamak discharges k_B⋅ T_e ≪ m_e c². Assuming Ohm's law (E = η⋅j) and Spitzer resistivity (η ∝ T_e ^−3/2) one finds that ξ (from equation (1)) scales with the ratio of E to E_D, with ξ being roughly five times E/E_D. Thus the streaming parameter could be used as a proxy for the available at.

Terminology related to fast electrons in a tokamak discharge is often confused. Supra-thermal particles are part of a non-thermal discharge (i.e. ξ > 0.2), however, such particles are not necessarily the same as RE. During tokamak plasma initiation, the discharge may be non-thermal and part of the electrons can be accelerated to relatively higher energies. However, the electron energies may still be limited (<100 keV) due to large losses and time limitations [1]. Later, when the discharge current increases and closed flux surfaces form, the confinement of fast electrons improves, and if still E > E_c, larger populations of actual RE can build up that eventually nearly all reach relativistic speeds. In such a case one can state that the current density, carried by RE is:

$$\begin{equation}{j_{\text{RE}}} = e\,\,{n_{\text{RE}}}\,c.\end{equation} \tag{ 4 }$$

Here, n_RE is the RE density in the discharge. Note that although for RE the collisional drag is less than their acceleration force, RE still experience collisions, as is obvious from the secondary generation mechanism. But RE can also collide with impurities and neutral particles in the plasma which is known to affect the generation and loss processes of these particles [10–14]. If RE can do damage does not depend on if RE can exist or can be generated in a discharge, or how much kinetic energy each RE could have, but depends on how much current is carried by the RE (I_RE) and the magnetic energy this represents [15].

RE can exist if E > E_c, but this criterion does not say anything about how many RE are present in the discharge. For this one has to determine the balance between the generation and losses of RE [3, 16]:

$$\begin{equation}\frac{{d{n_{\text{RE}}}}}{{dt}} = \,{S_{\text{primary}}} + \,{n_{\text{RE}}}{\gamma _{\text{secondary}}} - \frac{{{n_{\text{RE}}}}}{{{\tau _{\text{RE}}}}}.\end{equation} \tag{ 5 }$$

This equation can be converted into one for the change in j_RE using equation (4). This considers a primary and secondary RE generation mechanism which are explained in the next two paragraphs, respectively. The third component in equation (5), relates to the RE confinement time, τ_RE. A factor that may change significantly as the tokamak discharge progresses, as in section 2.3.

The primary generation of RE, S_primary, from a background electron population with a density n_e, temperature T_e, and effective charge, Z_eff, is usually given as [7, 16]:

$$\begin{align}{S_{{\text{primary}}}} &= n_{\text{e}}^2\frac{{{e^4}{} {\text{ln}}{} \Lambda }}{{4\pi \varepsilon _{\text{o}}^2m_{\text{e}}^2{c^3}}}{\left( {\frac{{{m_{\text{e}}}{c^2}}}{{2{k_{\text{B}}}{T_{\text{e}}}}}} \right)^{3/2}}{\left( {\frac{{{E_{\text{D}}}}}{E}} \right)^{3\left( {1 + {Z_{{\text{eff}}}}} \right)/16}} \nonumber\\ &\quad \times\exp \left( { - \frac{{{E_{\text{D}}}}}{{4E}} - \sqrt {\frac{{\left( {1 + {Z_{{\text{eff}}}}} \right){E_{\text{D}}}}}{E}} } \right).\end{align} \tag{ 6 }$$

It assumes that the background electrons are distributed Maxwellian with a temperature T_e. Those electrons with sufficient energy can become RE and these leave the background population. These are then replaced by other electrons via energy-space diffusion, restoring the original background electron distribution function. The primary generation is a very strong non-linear function of E/E_D, and one can show that primary generation becomes insignificant when E/E_D < 0.013 [17]. Based on the relationship between this ratio and the streaming parameter, plasmas with ξ < 0.065 have no significant primary generation. Effective primary generation, i.e. RE growth that provides a RE current increase significant with respect to the total tokamak discharge current may require values of ξ ≫ 0.065. This will allow us to provide a straightforward check on when this process is active or not. This process becomes more complex, when the background distribution is to be considered non-Maxwellian from the start, or when this thermal distribution changes, for example when T_e increases rapidly as is expected during the plasma initiation process in a tokamak [14].

The secondary, avalanching growth rate, in equation (5) can be given as [16, 18]:

$$\begin{equation}{\gamma _{{\text{secondary}}}} = \sqrt {\frac{\pi }{{3\left( {5 + {Z_{{\text{eff}}}}} \right)}}} \frac{1}{{{} \ln \Lambda }}\frac{e}{{{m_{\text{e}}}c}}\left( {E - {} {E_{\text{c}}}} \right).\end{equation} \tag{ 7 }$$

Here collisions of high energy incident RE with the background electrons create new, secondary, RE, that could result in an avalanche effect. Note that for secondary generation in a partially ionized plasma, the calculation of E_c, to be used in the above equation, should consider as n_e, the density of both free electrons and bound electrons [18] and also modify the Coulomb logarithm to include bound electrons [16].

The above two equations are all derived under certain conditions and with certain assumptions. The primary growth assumes a Maxwellian energy distribution for the background electrons in a plasma that is fully ionized, for which part of the population shifts towards relativistic RE. But during the early stages of a tokamak discharge, the assumption of a Maxwellian distribution does not apply. Moreover, the presence of neutrals in a not fully ionized plasma may slow the RE generation [1]. Similarly, secondary generation as derived above assumes RE can freely increase and that the incident RE have infinite energy [18], while the incident RE energy may actually be limited. This would mean that the secondary generation according to the above equation might be overestimated, especially for cases when E is only slightly above E_c [19–22], as also was observed experimentally [5].

Finally, the growth of the RE population, given by equation (5), will need to compete with the growth of the thermal population. This is a significant difference with RE generation after a tokamak discharge disruption, when the thermal plasma collapses (i.e. a fast decrease of T_e, to very low values of a few eV) combined with a quench of the current, the latter increasing E. The change in j_RE is given by equations (4) and (5). However, this is coupled to the dynamics of the thermal current, j_TH, via the circuit equation:

$$\begin{equation}\,{V_{\text{L}}} = I \cdot R + {L_{\text{tor}}} \cdot \frac{d}{{dt}}I = {V_{\text{R}}} + {V_{\text{I}}}.\end{equation} \tag{ 8 }$$

Here the total current, I = j⋅A_c, where A_c is the poloidal cross-section of the plasma and j = j_TH + j_RE. L_tor is the inductance of the toroidal plasma, with V_I being the inductive voltage and V_L being the externally applied loop voltage, and R being the resistance. Parameters such as A_c and L_tor are, for simplicity, assumed constant in time, but these may change considerably during the plasma initiation process. V_R is the resistive voltage which is related to the electric field, E as E⋅2⋅π⋅r_o = V_R, where r_o is the device major radius. It is this E that generates RE and enters the primary and secondary growth rates given above. Note that it is usually assumed that the resistive voltage is equivalent to I_TH⋅R_TH. As is shown in [5], a fast increase in total current, I, either due to a controlled ramp of the thermal current, or a too fast increase in j_RE, will reduce, via equation (8), V_R, thus E, and as a result, limit the growth of RE. Note, that one cannot neglect V_I, in the absence of any thermal plasma, for example when the discharge has converted to a full RE beam, and I = I_RE. Equation (5) shows that even for a constant value of n_RE and thus j_RE, one needs some RE generation to compensate for the losses, hence a value of E > 0. Indeed, under such circumstances the RE discharges were shown to require a small V_I and V_L, to maintain a constant current [5].

The critical issue with start-up RE formation, is not if they form, thus if E > E_c, or if one obtained positive growth from equation (5), but if sufficient RE are formed that (1) their dynamics affect equation (8), and other aspects of the thermal plasma, (2) RE can damage in-vessel components as has been noted before. The first point would be met if simply j_RE ∼ j, although already before that, significant levels of j_RE would reduce j_TH and thus also reduce the ohmic heating that is relevant to maintain the thermal plasma, eventually leading to a collapse of the thermal plasma and the formation of a full RE beam, i.e. all current is carried by RE [5]. The second point would mean that I_RE reaches a critical value that in part may depend on the wetted area on which the RE energy is deposited [15].

To calculate the full dynamics of start-up RE, one needs to solve the coupled equations for the RE generation and RE and thermal currents, further coupled with the development of the thermal plasma, that describe the dynamics of the n_e and T_e, and the linked resistance, similar as is done in some plasma initiation simulation codes [6, 23, 24].

RE are expected to have high energies and as noted above, however, it takes time for these particles to gain energy. It is worth looking into, how long it takes for them to reach certain energies, and what may limit their energy in the end. It takes 5–12 ms for an electron to be accelerated to 95% of the speed of light, c if it experiences an electric field of E = 0.7 V m⁻¹ and E = 0.3 V m⁻¹, respectively [5]. For higher energies, the energy of a relativistic RE being accelerated by an electric field E(t) can be approximated as:

$$\begin{equation}\gamma \left( t \right)\sim \int\limits_{{t_{\text{o}}}}^t {\frac{{e{E}}}{{{m_{{\text{eo}}}}c}}} {\text{d}}t = \int\limits_{{t_{\text{o}}}}^t 5 87 \cdot E\left( t \right){\text{d}}t.\end{equation} \tag{ 9 }$$

Here, γ is the relativistic correction factor. The RE energy, W_RE, in units of MeV, is given by the conversion: W_RE(t) = 0.51⋅(γ(t) − 1) in MeV. If the thermal plasma develops well and becomes more conductive, the discharge would have a small V_R and thus low value E, hence it might take a considerable time for RE to gain multiple MeV energies.

The duration of the acceleration is however limited by the time during which the RE is confined, i.e. τ_RE. This will set a limit to the maximum energy that can be achieved by RE during the current ramp-up. Early in the tokamak discharge, when characteristic closed magnetic flux surfaces (CFSs) have not yet formed, relativistic RE may not be able to exist, simply due to the fast parallel losses of such particles. Prior to the formation of any local CFS, only very limited energies (i.e. several 100 eVs) can be achieved [1]. Hence, t_o in the above equation is best considered as the time when CFS form. The next energy limitation that is traditionally quoted to be relevant to start-up RE, relates to so-call drift orbit (DO) losses. For highly energetic RE, the DO will be such that they intersect with the vacuum vessel, and thus such particles will be lost [2, 25, 26]. Assuming a constant distribution of current density, for a given total current, I, a maximum RE energy for which the trajectories remain within the tokamak, is given by [2, 27]:

$$\begin{equation}\gamma _{{\text{max}}}^{{\text{DO}}}{} \sim 118\; \cdot \frac{{{r_{\text{o}}}}}{{{r_{{\text{out}}}}}}\left( {1 - \frac{{{r_{{\text{in}}}}}}{{{r_{{\text{out}}}}}}} \right){} \times I{} \sim {} 118 \cdot {} {F_{{\text{geom}}}}{} {} \times I{} .\end{equation} \tag{ 10 }$$

Here, I is in MA and r_out is the radial position of the outer limiter that intersects with the RE trajectory and thus where it is lost, while r_in, is the location where the RE is formed, which could be considered the plasma centre (r_o) or further inward. Both r_in and r_out are related to r_o, and a, the plasma minor radius. It can be shown that the geometric factor for most tokamaks is of the order of F_geom ∼ 0.2–0.4 and that it scales approximately with the inverse aspect ratio, ε = a/r_o. For more peaked current profiles, the DO are slightly better confined [2].

As the current ramp-up progresses, according to equation (10), the confinement of higher energy RE improves. However, microscopic or macroscopic magnetic field perturbations, such as the magnetic field ripple, are known to affect RE motion as well, limiting their life-time in the plasma, and thus the maximum energy they can obtain. If RE reach energies of several MeV, direct energy loss due to synchrotron emission starts to dominate and thus determine the maximum energy they can obtain [27, 28].

One of the key time scales concerns the RE confinement time, τ_RE, as used in equation (5). The previous section (section 2.3) has already alluded to the connection between τ_RE and the maximum RE energy.

The time, non-relativistic electrons can be accelerated along open field lines (OFLs) of a length, L, is equal to [4]:

$$\begin{equation}\tau _{\text{RE}}^{\text{OFL}} = \,\sqrt {\frac{{2\,L\,{m_{\text{e}}}}}{{e\,E\,}}} .\end{equation} \tag{ 11 }$$

This can be considered a confinement time, prior to the formation of any CFS. For E = 0.3 V m⁻¹ and L = 10 000 m, this gives times that are sub-milliseconds. Under these circumstances, electrons are unlikely to reach very high energies, which are usually limited to well below the MeV level.

But, as noted in the previous section (section 2.3), when CFS form their confinement improves significantly. RE can now be confined up to the point they are accelerated to such high energies that their DO become too large. Assuming a constant acceleration (i.e. E) and constant value of I, from equations (9) and (10) a confinement time can be derived:

$$\begin{equation}\tau _{{\text{RE}}}^{{\text{DO}}}\sim 0.2{} {} \cdot {F_{{\text{geom}}{} }}{} \cdot \frac{I}{{{} E}}{} \cong 1.25 \cdot {r_{\text{o}}}{} \cdot {F_{{\text{geom}}{} }} \cdot \frac{I}{{{V_{\text{R}}}}}.\end{equation} \tag{ 12 }$$

Here, the current I is in units MA. For I = 1 MA and V_R = 0.2 V, and r_o = 3 m (i.e. JET start-up values), this confinement time is of the order of τ_RE ^DO ∼ 6–10 s. This value should be considered an order of magnitude estimate for τ_RE ^DO and larger confinement times for JET have been found [5]. This confinement improves linearly with the total current, thus RE confinement due to DO losses would improve as the current ramp-up progresses. From the above equation, one can deduce that this confinement times scales stronger than linear with the device size (i.e. r_o), because the device current I, also is a function of its size.

But other loss mechanisms exist. Micro-scale magnetic turbulence in the plasma is capable to diffuse RE orbit from the core of the plasma towards the edge [29]. This so-called Rechester–Rosenbluth (RR) diffusion depends on the level of magnetic turbulence, δb, relative to the total magnetic field, B_T: b = δb/B_T. This effect varies per device and depends on the RE energy as well [27, 30]. The relative level of magnetic turbulence in a tokamak discharge is estimated to be of the order of b ∼ 10⁻⁴–10⁻² [30]. A confinement time can be derived from the diffusion coefficient, D^RR that is thought to be proportional to the b², the RE speed, which is assumed to be the speed of light, and the distance the RE travels through the plasma, estimated to be ∼ π⋅q⋅r_o [29]:

$$\begin{equation}\tau _{\text{RE}}^{\text{RR}}\sim \,\frac{{{a^2}}}{{{D^{\text{RR}}}}} \sim \frac{{{a^2}}}{{\pi \cdot q \cdot {r_{\text{o}}} \cdot c \cdot {b^2}}}\alpha \frac{1}{{\,q\,}}\frac{{{a^2}}}{{\,{r_{\text{o}}}\,}}{b^{ - 2}}\,\alpha \frac{I}{{\,{B_{\text{T}}}\,}}{b^{ - 2}}.\end{equation} \tag{ 13 }$$

Here, q is the safety factor. For this loss mechanism, the confinement time is shorter for a higher level of b. Note that in this case, the exact values of this confinement time are more difficult to assess. Not only because the level of b is not well known, but also because of the arbitrary assumed value of S. Moreover, RE diffusion is affected by their energy [30] and this is thought to be related to the partial de-correlation from the magnetic turbulence, at higher RE energies [31]. Hence, corrections to the above equation (13) are needed that reduce the losses of higher energy RE. It is therefore difficult to accurately assess the value of τ_RE ^RR. It has been reported that the RE diffusion can vary between D^RR ∼ 0.001–1 m²s⁻¹ [30] and in JET would be of the order of D^RR ∼ 0.03–0.2 m²s⁻¹ [5, 31] suggesting for JET τ_RE ∼ 4–20 s, which is similar to the value estimated for drift-orbit (DO) losses. Equation (13), gives some insight into how this RE confinement time scales from device to device. If one assumes that the level of magnetic turbulence is smaller in larger devices, this would again suggest that this RE confinement time scales stronger than linear with the device size. Interestingly, this confinement time would also increase during the current ramp-up, via its relationship with q.

None of the above mechanisms takes into account RE losses due to short bursts of macro-scale Magneto-HydroDynamic activity or possible non-linear RE-plasma wave interaction that may occur during plasma initiation or the early current ramp-up phase [32–37]. These effects could result in short bursts of RE losses, decreasing the average overall RE confinement.

The above time scales on which RE can be formed and lost can be compared to a number of other basic time scales relevant to plasma initiation and tokamak start-up. According to the circuit equation (equation (8)), the (RE) current rise is always limited to:

$$\begin{equation}\frac{d}{{dt}}I < {V_{\text{L}}}/{L_{{\text{tor}}}}.\end{equation} \tag{ 14 }$$

Thus from equations (4) and (5), one can show that there is a simple limit to the primary growth rate, S_primary, as E/E_D is limited, under tokamak start-up conditions. This is opposite for RE generated during a disruption, for which the quench of the current, in contrast to an increase I, actually drives the electric field, thus much higher values of E/E_D can be achieved, than the limit shown here. The above equation will also set a limit to the time large RE beams can develop during start-up conditions.

A second important time scale is the duration of the current ramp-up, Δt_ramp-up, which scales with the resistive time as, τ_R, as:

$$\begin{equation}\Delta {t_{\text{ramp} - {\text{up}}}}\,\alpha \;{\tau _{\text{R}}} = \,{\mu _{\text{o}}}{a^2}{\eta ^{ - 1}}\alpha \;{a^2} \cdot \,{Z_{\text{eff}}} \cdot T_{\text{e}}^{3/2}\end{equation} \tag{ 15 }$$

where η is the plasma resistivity (i.e. Spitzer resistivity, assuming a predominantly Maxwellian electron energy distribution). As will be shown later, the duration of the RE generation and dissipation process often far exceeds the plasma initiation stage, and continues long into the current ramp-up for most tokamaks.

In figure 1(a), the spread off all cases in the database, in the parameter space of E_L versus the prefill pressure, p_n, at the time of breakdown is shown. Here E_L is the externally applied toroidal electric field in the centre of the device, equivalent to V_L/2πr_o. Some of the cases do not show clear signs of RE activity, others do, thus figure 1(a), shows that there is not a direct relationship between the range of E_L or p_n and the observed RE activity. The figure merely shows the general range at which the devices operate their breakdown and plasma initiation and both cases that form strong RE signs and those that do not show clear signs of RE fall in similar areas. Interestingly, it also shows that the super-conducting device KSTAR has breakdown conditions that are close to those of ITER. The ITER cases, in figure 1, are from a series of simulations of ITER plasma initiation, using the SCENPLNT code [6]. The cases studied here can be spit up, by those that have generally a lower E_L (i.e. here JET, NSTX, KSTAR and ITER) and those that have been achieved with a higher E_L (i.e. FTU, WEST, C-MOD).

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Here, only the cases that make up this specific database are shown, and the plasma initiation operation range is usually larger, as can also be seen in [5, 47]. The full device operation range was provided for all devices in the database, and the range of the ratio E_L/p_n, and these ranges are shown in figure 1(b). Most devices have operated around the ITER operation point of 300 V m⁻¹ Pa⁻¹ (for E_L = 0.3 V m⁻¹ and p_n = 1 mPa). For the C-MOD case, RE are generally observed if available at: >400 V m⁻¹ Pa⁻¹. However, the specific RE case supplied to this study had much lower values. Also, the cases chosen for NSTX, KSTAR and JET, for which several showed clear signs of RE, are actually near the lowest limit of the E_L/p_n range. It suggests that value for E_L/p_n does not seem to be of importance for start-up RE formation. No clear E_L or p_n range can be indicated, general to all devices, for which start-up RE would form.

During the tokamak start-up, the current dynamics should obey equation (8), hence setting an absolute limit to the maximum possible current rise, in the tokamak, given by equation (14). This limit depends on the applied loop voltage and the size of the device, via A_c and L_tor. In figure 1(c) is shown that this also sets a limit to the maximum possible value of E/E_D. This maximum is determined by finding the value of E/E_D for which e⋅c⋅S_primary(E/E_D) = V_L⋅L_tor ⁻¹⋅A_c ⁻¹ for a fixed value of T_e, here chosen to be 100 eV and Z_eff = 2, typical for the early current ramp-up. For practical reasons, this limit is converted in the maximum value of E/E_c, for a fixed T_e = 100 eV as shown in figure 1(d). Higher values of E/E_D and E/E_c (for T_e = 100 eV) are not possible. For higher values of T_e, the E/E_c limit decreases while the maximum value of E/E_D increases. Interestingly, the variation of the maximum value of E/E_D and E/E_c is significantly smaller than the range of values of V_L⋅L_tor ⁻¹⋅A_c ⁻¹, because S_primary scales strongly with E/E_D. This absolute maximum of E/E_D for tokamak start-up is always well below unity, while the maximum for E/E_c is of the order of 10². Secondary generation at this very early stage of the discharge may not be relevant yet, because not sufficient RE seed might have built up. However, it is worth considering that for very high values of E/E_c, the secondary growth rate might well be higher than that given by equation (7) [56].

In figures 2–4, a few cases of each device are shown, one or more that develop strong signs of RE (often shown in red), another with very similar E_L and p_n, for which no RE are detected (shown in green), and for some devices, an intermediate case (shown in yellow), for which RE are observed, but these dissipate later in the discharge. This point is also an important feature of start-up RE: they can form, and increase but also dissipate and decrease on a time scale shorter than Δt_ramp-up. This again means that in such cases, the RE density growth as given by equation (5) becomes negative, either because of negative secondary growth or too short a confinement time. A detailed look into the figure will show that the dynamics of a number of parameters, such as the streaming parameter, the resistive electric field E, and the density all matter in determining if RE become prevalent or not. Most devices show striking similarities, while there are also differences. Specifically for JET, one case (80263), shows the generation of a discharge for which the current is carried fully by RE, as reported in [5]. The initial development of this discharge is indistinguishable from the preceding case 80262, which only showed moderate and temporary signs of RE. This last case is close to JET discharge 81231, also shown, which was analysed in detail in [45], showing that in this case, the I_RE increased and peaked at I_RE ∼ 40 kA (approximately 2%–3% of the total current) before dissipating slowly.

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For each device a different time window is shown, focussing on the approximate duration of the current ramp-up. This differs for each device, being significantly longer for larger, devices, as the current ramp-up time, in general, scales with the current diffusion time. The total current density, j, per device also varies, with those devices that operate at a higher B_T, also having a larger, j.

The first observation relates to the behaviour of the ratio of E/E_c, which for most devices is well above unity at the time of plasma initiation but gently decays to lower values as the current ramp-up progresses, although it never seems to fall below unity. The general trend for the decrease of E/E_c during the tokamak start-up is due to the general increase in n_e, combined with an increase in T_e, thus a reduction in E. An exception is NSTX which provided cases that suggest an increasing value of E/E_c over time, linked to the decreasing value of n_e/j. The latter is purposefully done, to experimentally generate RE during the start-up. The reason for the noisy traces for nearly all devices is that in order to determine the value of E, the inductive voltage has to be subtracted from the measured externally supplied electric field, and inaccuracies in the knowledge of the value of L_tor, and the determination of the derivative of the total current, add up to large errors in the value of E. Nevertheless, one can state that all of these devices seem to operate during the current ramp-up with E/E_c > 1, an aspect that will be looked into further, in section 4.

Secondly, the behaviour of the streaming parameter shows, that all devices show to be non-thermal (i.e. the streaming parameter higher than 0.1 are common at this stage of the discharge) at the time of plasma initiation, but in general the discharges thermalize (i.e. ξ < 0.05) around about a tenth of the duration of the current ramp-up, especially those, that do not have any significant signs RE activity. It suggests that all cases are non-thermal around the time of plasma initiation, i.e. the electron energy distribution is non-Maxwellian, though it does not mean there is yet a significant RE population. For a few notable cases, the streaming factor starts to increase again well above ξ > 0.1 later in the current ramp-up, while also measurements of RE activity are high. The latter suggests a dangerous non-thermal discharge, likely with a large fraction of the current carried by RE. In these figures, such cases are shown from NSTX and JET, but similar cases also exist, for example, for C-MOD. Note that for all devices, the RE activity increase (generation) and dissipation (losses) extend well into the current ramp-up phase. Thus start-up RE is definitely not a mere plasma initiation issue. It should be reminded that dynamics of ξ are a proxy for those of E/E_D, dynamics as noted in section 2.2.

The final point relates to the behaviour of the dimensionless parameter n_e/j. It is nearly equivalent to the Greenwald fraction, f_GW [57], but this ratio is also known from the early days of tokamak operation as an indicator for the presence of RE activity [2, 58]. The ratio is inversely proportional to the streaming parameter and is often seen as more practical to calculate as it would not require T_e. Discharges with low values of n_e/j are known to be prone to RE activity, which is also clear from figures 2–4, for the NSTX, KSTAR and WEST cases, for example. However, no clear separation is visible, and no clear criterion can be given for a value of n_e/j, above which RE activity would not be seen.

Besides collecting and comparing measurements, the survey also collected general experiences, related to start-up RE, which will be summarized here. Although one may perceive these points as conjectures that are not necessarily backed by actual scientific studies, it was thought that listing these observations, often found at multiple devices, are important to prepare ITER plasma operation such that one prevents too strong RE activity during its start-up. The following observations were made:

Start-up RE observations are often found when a tokamak carries out its first plasma operation or first operation after a major upgrade. The plasma start-up dynamics, and especially that of the density, may differ from what is expected during such first operations. Such differences in density behaviour led to start-up RE, when JET transitioned from a carbon-wall to a beryllium main chamber wall [5, 59, 60], and this was also observed during first operation of WEST that used a full tungsten wall [48]. Differences in recycling in tokamaks with full metal walls can lead to lower-than-expected densities during the early stages of the tokamak discharge, generating start-up RE. But such events were gradually prevented in both devices after careful tuning of the waveform requests and changes to density control. A link with device conditioning that improves gradually after first plasma operation, is also possible. Erroneous tokamak control actions, especially related to the density control or the continuous application of V_L that keeps the RE formation going, can make things worse, as has been seen in JET [5]. In general, a strong relationship between the occurrence of RE activity and the density or Greenwald fraction: too low a density (due to low prefill pressure, density control problems, too high pumping (e.g. during X-point formation, wall recycling) is observed. Already in the early days of tokamak research, it was known that a higher value of I/n_e seems to make start-up RE more likely [2]. For smaller devices, the prefill is often the key factor to control the density during the plasma initiation or early start-up, but for larger devices density control and wall conditioning may become more relevant. The influence of plasma impurities on the RE formation was already noted in section 2, but not further pursued in this study, because this is better done, in a single-device experiment, allowing easier comparison of impurity measurements.

Tokamak discharges with and without start-up RE activity are difficult, or sometimes impossible, to separate. Most of those that show early signs of supra-thermal or REs (e.g. supra-thermal electron cyclotron emission (ECE) or hard-x-rays), thermalize later during the ramp-up stage (i.e. RE activity diminishes). In rare occasions, however, the number of RE increases to such an extent that their loss damages in-vessel components. Many of the discharges that show signs of RE during the start-up do not cause problems or damage. Their presence might often be overlooked. It is not the presence of RE themselves, but the amount of RE that is generated that is the problem. It has been known that disruptions during the current ramp-up, are more prone to form large RE beams, compared to when this happens during the flat-top phase of the tokamak discharge. This might be interpreted by the presence of some RE seed, during all tokamak current ramp-up.

The conversion of the entire current being carried by RE is a worst-case scenario, which obviously leads to damage when such RE beams are lost and the energy is deposited on in-vessel components, as has been seen at JET [5]. However, even without such a conversion to a full RE beam, start-up RE can cause damage. At the start of WEST operation RE generated during plasma initiation were able to damage in-vessel components, generally simultaneous with the quench of the current, either due to burn-through problems, or when the plasma disruption in the early stages of the discharge [48, 49, 52].

Tokamak plasma initiation is often supported by means of radio-frequency (RF) heating methods, such as ECH. It is known that the wave electric fields of these heating methods are capable to accelerate electrons to high energies [61], hence, the application of RF heating can provide an additional RE generation mechanism. However, an accurate ECH RE source model is not yet available. Experimental evidence of such a source has been reported [41, 42]. On the other hand, auxiliary heating in general might also provide a beneficial effect by augmenting the plasma temperature and hence decreasing its resistivity and thus the required E during the current ramp-up, which aspect is shown in more detail in section 4.

There is a big variation in the method of diagnosis of RE and the accuracy of detection varies. This makes a general classification, device comparison or benchmarking of simulations difficult. RE are usually observed (e.g. by supra-thermal ECE, neutrons that are emitted, or hard x-rays/gamma rays [2]) even while the streaming parameter indicates that the plasma in general terms is thermal. However, all these diagnostic methods, only indicate more RE are present in one discharge compared to another, but this difference is rarely quantifiable, nor is it possible to compare observations from devices. Such issues with diagnosis can also result in a misinterpretation of the RE detection, as the qualitative detection method may not be able to correctly determine the risk of damage due to RE.

The second aspect to investigate concerns the behaviour of the streaming parameter. As is shown in figures 2–4, for most devices, the streaming parameter suggests a far from thermal plasma, during and right after the plasma initiation, even for those cases that later do not show any clear RE activity. For all cases, the streaming parameter, ξ, decreases rapidly, indicating a thermalization of the discharge. As explained in section 2.2, the value of the ξ is linked to E/E_D and for too low values ξ < 0.065, primary generation would become negligible. The streaming parameter is easier to determine experimentally, while the value of E/E_D is prone to large errors in the determination of E, as noted in section 3.

In figure 6(a), the time for which ξ decreases after plasma initiation below a value 0.065 (t_{ξ < 0.065}) is shown for all cases (including those that do not show clear RE signs). The ordering by Δt_ramp-up seems to work again. Roughly, the primary generation becomes negligible 10% into the current ramp-up (at t = 0.1–0.9× by Δt_ramp-up). But there is, per device, quite some variation. These variations in t_{ξ < 0.065} are due to differences in the detailed behaviour of n_e and T_e, with respect to the current rise. Those cases, for which this specific time is longer, will generate a larger seed of RE by primary generation. This is clearest seen for specifically KSTAR as shown in figure 6(b). The KSTAR values of t_{ξ < 0.065} for the cases in the database vary nearly one order of magnitude. For those KSTAR cases for which t_{ξ < 0.065} is the longest, RE are detected earliest. Thus most cases that show clear and early signs of RE activity lie at the upper part of figure 6(a), however, a clear trend, as is seen in KSTAR, is not found in all devices. Variations in the observations of RE, are not only due to the strength and duration of the primary generation but can also be caused by differences in the secondary generation that can enhance any seed, even weak. In figures 2–4 it can be seen that in some cases, ξ starts to increase again, to higher values later in the ramp-up. These cases will be discussed in more detail in section 4.5. In figure 6(a), those cases for which RE losses are known to have caused damage (as indicated in bold in table 1), have been labelled specifically. The WEST case with a short value t_{ξ < 0.065} contrasts here against the two JET cases and the C-MOD example.

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During the current ramp-up phase usually n_e increases while E decreases, as the thermal plasma resistivity decays with an increasing temperature. Although there are some counter-examples shown in figures 2–4, for example for NSTX and FTU, for which the ne is kept (intentionally) at very low levels. For all cases, the average value of E, and n_e have been determined over a time interval from 0.1 to 0.9 × Δt_ramp-up and these values are shown in figure 7(a). This averaging reduces the large error in the measurement of E. Error bars are added in figure 7(a ) to indicate the temporal variation in E and n_e during the averaging time interval. The two cases of DINA simulated ITER ramp-ups to I = 15 MA have also been included for comparison. As obtained from figure 1(d), the upper boundary is set by the values of E/E_c (∼150–250) during the plasma initiation (thus prior to 0.1 × Δt_ramp-up). But soon after plasma initiation, the values will have to decrease below E/E_c < 50. Above this value, it is possible to obtain primary RE generation that yields a RE current increase that would violate the criterion set by equation (14). Figure 7(a) shows that the values of E/E_c (averaged over the current ramp) generally fall in the range E/E_c ∼ 10–30, suggesting secondary generation could effectively enhance any RE seed. The only exceptions are the largest devices JET and ITER, for which E is close to or just below E_c. NSTX shows the highest values of E with respect to E_c. But as is shown in figure 2, the density is purposely decreased during the current ramp-up of the NSTX cases, to create circumstances for RE formation.

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Figure 7(a) can be normalized by total current density j, which converts the y-axis into the averaged resistivity and the x-axis a value similar to the Greenwald fraction, f_GW, as is shown in figure 7(b). If the resistivity values are plotted against the device size (r_o) as is shown in figure 7(c), it becomes clear that larger devices, with higher T_e, operate at lower values of E during the current ramp-up. Less clearly visible, is the feature that devices with a higher B_T, such as C-MOD and FTU, operate generally at higher n_e, thus lower T_e, and consequently higher values of E. Notably, the ITER case that makes use of ECH during the current ramp-up is the one that shows the lowest value of E and the lowest value of η.

The secondary growth rate is theoretically predicted to depend on E − E_c. And this difference between E and E_c is shown in figure 7(d), to decrease significantly with the device size. It has been avoided here, to show the trend with calculated values of the secondary growth rate, using equation (7), because the raw data of E − E_c, provide more insight by themselves, without adding the additional assumption on the growth rate equation. Using equation (7), one can calculate that for the smallest device size in the database, γ_secondary ∼ 5–10 s⁻¹ while for ITER this decrease to γ_secondary < 0.1 s⁻¹. And note that it is known that for E < 2⋅E_c, finite energy effects may further reduce the secondary RE generation process with respect equation (7) [19–22]. The trend is clear that, irrespective of the value of τ_RE, for devices such as ITER, secondary generation may become negligible due to the levels of T_e, n_e and E during the current ramp-up.

The density is not a completely independent parameter that can control the RE formation, by for example increasing E_c or E_D. Increasing the density might reduce j/n_e, and increase E_c, but for an Ohmic plasma initiation and current ramp-up, increasing n_e will reduce T_e, and thus increases E. Therefore, a higher n_e will therefore not necessarily reduces RE generation. Experiments at WEST showed that high prefill pressure operation, and too high a density, enhanced RE generation in combination with a failure of the plasma initiation to burn-through. To reduce both primary and secondary RE generation, both n_e and T_e need to be ramped up throughout the plasma initiation and current ramp-up process.

As pointed out in section 3, the use of ECH during plasma initiation has been identified to provide an additional RE source mechanism. The efficiency of this RE source compared to primary or secondary generation is generally not yet well understood. However, comparing FTU discharges with similar values of E/E_D, thus likely a similar primary generation level, but with or without ECH power, showed that those with ECH power produced more RE [41, 42]. However, experiments also show that the application of ECH, generally results in lower levels of E/E_D in general, due to the higher plasma temperatures. Using auxiliary heating, such as ECH during the plasma initiation process, to assist burn-through, and during the current ramp-up, allows one to operate at both higher T_e, and higher n_e. The higher T_e, for a given n_e, will effectively reduce E/E_D and E/E_c. The two ITER ramp-up simulations that are added as a comparison to for example figure 7(a), show that ITER has a low value of E, for an Ohmically heated ramp-up but this can be reduced below E_c, if ECH is applied. Figure 8 compares this in more detail, showing two KSTAR discharges, one with and another without the use of ECH. The trend for the streaming parameter, ξ, is roughly the same, but the application of ECH allows operation at lower n_e, albeit generating significantly lower hard x-ray emission (an order of magnitude less) and hence, less RE.

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The previous results (in section 4.1) showed that for nearly all cases, primary generation becomes negligible after at least 0.1 × Δt_ramp-up, thus, in general, the RE dynamic during the current ramp-up of most tokamak discharges is determined only by secondary generation and RE losses. For a few specific cases, as is shown in figures 2–4, a reduction in the RE activity is observed (i.e. the signal intensity reverses and starts to reduce). This indicates that for these specific cases, at the time the RE signal intensity reverses, according to equation (5), secondary generation and RE losses are balanced. Under the assumption of equation (7), based on the values of E and E_c (n_e) one can determine the value of the RE confinement time, τ_RE. Although, this may provide an overestimation of τ_RE if E_c < E < 2E_c [19–22].

Thus a subset of the database, concerning specific cases, that show a reversal, or a much-reduced growth of the RE signal, was created. In figure 9, the estimated values of τ_RE, are shown. The best trend with the major radius suggests a scaling of r_o ^+2.57. As noted in section 2.4, both candidates; τ_RE ^DO and τ_RE ^RR suggest such a stronger than linear scaling with r_o, as is observed here. Although the values for both candidate confinement times are in the range with the observations here. Unfortunately, this analysis does not provide a clear indication which of these two loss mechanisms is relevant here. But it gives a good idea of the value of τ_RE in various devices and indicates that in ITER, during the current ramp-up, τ_RE would be approximately a factor 5 larger than in JET, while JET features values of τ_RE ∼ 5–20 s. If these confinement times would be compared with the duration of the current ramp-up one would find, that for the smaller devices, τ_RE is a smaller fraction of Δt_ramp-up, while for larger devices, such as JET, they are of the same order of Δt_ramp-up. Thus, with respect to the typical current ramp-up time, RE are relatively better confined in ITER compared to most of nowadays devices. And thus, if they are formed, more difficult to dissipate. The times shown in figure 9 apply roughly during the mid-current ramp-up. Under the assumption, of either equations (12) or (13), it is likely that the RE confinement is lower earlier in the discharge (when the current is lower).

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All cases provide information on E(t) albeit often with a large error, although the error reduces as the current ramp-up progresses. This allows us to calculate the maximum energy a RE could obtain assuming it is freely accelerated by this field, using equation (9). Actually, to stay with the comparison of time scales, one can reverse equation (9) and determine the time needed to reach a certain energy. Figure 10(a) shows the time needed to achieve W_RE = 10 MeV, i.e. t_{W = 10 MeV}, for each of the cases in our dataset, including again the two simulated ITER cases. The data has been obtained by integrating the increase of the RE energy (using equation (1) not from t = 0, but from the time CFS are formed. It shows that this time is shorter for devices that apply a large E_L. For ITER t_{W = 10 MeV} is longer than for KSTAR, although they have the same E_L, however, relevant here is V_R and E and their temporal behaviour after breakdown, with E generally being a decreasing function of time, as T_e increases. From figure 7(a) it is clear that larger devices ramp up at lower E, thus a device like ITER needs more time to obtain the same RE than a device like KSTAR.

This may give the impression, it is more difficult in ITER to reach higher energies. However, compared to the duration of the current ramp-up, t_{W = 10 MeV} in ITER is significantly shorter than in smaller devices, as shown in figure 10(b). In larger devices, it is possible to reach W_RE = 10 MeV in a fraction of the current ramp-up, while in smaller devices, like NSTX, this would require the entire current ramp-up. It is important to understand that especially for higher RE energies (i.e. W_RE > 10–20 MeV), losses due to synchrotron emission and other losses will become effective, clamping the further growth [27]. It is known that RE can achieve maximum energies of the order of 10–20 MeV in devices like FTU and JET [39, 44, 62].

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In section 2, losses due to too large RE DO are introduced. This assumes that RE gain energy quickly, such that their DO, which depends on the plasma current, intersect with the vessel. However, during the tokamak start-up the current is increasing, and the question is, how the RE energy increase compares to this current rise? It should be reminded, that a related value of τ_RE is derived (equation (1) for a constant E and I, i.e. assuming these values do not change over the time the RE is accelerated and lost. It is, therefore, worth comparing the time scales to gain a certain energy (by free acceleration) and at what time DO for a specific RE energy are confined. The latter depends on the growth of the current, I, according to equation (10). Figure 11(a) compares t_{W = 10 MeV} with the time by which the current is large enough to confine DO of RE with an energy of up to 10 MeV, at a location r_o, t_{WDO = 10 MeV}. It shows that in many cases these time scales are comparable and of the order of Δt_ramp-up. And thus the assumption that I and E are constant is not satisfied.

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If t_WDO < t_W, it means the current needed to confine the RE DO increased faster than the fastest (i.e. free) possible acceleration of the RE. Whether DO are possible is determined by the ratio of the maximum energy for which DO are confined, γ_DO(t) for a given value of I(t), to the maximum value of the energy that could be achieved by free acceleration in a field E(t), γ_max(t). It is usually assumed that at very low plasma currents DO losses are easiest, however, before the creation of CFS the maximum electron energy is limited. Thus in general, DO losses only become possible after the creation of CFS while also enough time should have passed for the electron energy (γ_max(t)) to increase such that γ_DO(t)/γ_max(t) reduces below unity. For many discharges in the database, γ_DO(t)/γ_max(t) starts above unity, but as the electron energy increases, it eventually decreases below unity and DO become possible. This is true for all cases in figure 11(a), for which t_{WDO = 10 MeV} < t_{W = 10 MeV} (i.e. for WEST, KSTAR, C-MOD and FTU and partly JET). However, for those that have t_{WDO = 10 MeV} > t_{W = 10 MeV} the ratio of γ_DO(t)/γ_max(t) remains above unity during the entire current ramp-up, and thus DO will never be possible (i.e. for NSTX, ITER and some JET cases).

Figure 11(a) shows a big variation per device. The difference here lies in that the current, a device operates at, scales as ε²⋅r_o⋅B_T, where ε is the inverse aspect ratio of the device and the loop voltage it applies. The geometric factor in equation (10) also depends on ε, thus tokamaks that operate at higher currents and have larger inverse aspect ratios, are able to confine RE drift orbits more easily, i.e. have a shorter t_{WDO = 10 MW}. While devices that operate at a higher V_L will quicker accelerate RE and thus have a shorter t_{W = 10 MW}. Figure 11(b) shows the scaling of the ratio of t_{W = 10 MW} and t_{WDO = 10 MeV} with an arbitrary scaling using these parameters. This of course does not capture the exact temporal dynamics of E(t) and I(t), but, nevertheless, explains the differences per device. For a larger device such as ITER, operating at a large plasma current but with a small loop voltage, RE DO are unlikely to be possible. The same is true for smaller devices but with a larger aspect ratio, such as NSTX. The selected JET cases, for this study, have a rather low V_L (see figure 1(a)) and for some JET cases, the ratio is above unity and thus DO losses are unlikely while for others, like C-MOD, FTU and KSTAR such losses are possible. This means that RE DO losses cannot be considered a standard and common RE loss mechanism. Such losses are only possible under specific circumstances and in smaller, lower aspect ratio devices.

In section 4.1 it was described that in general, the streaming parameter ξ decreases as a function of time, from a non-thermal situation at the time of plasma initiation, usually thermalizing about 10% into the current ramp-up. As noted in section 2, a high streaming factor means a non-thermal plasma, thus the energy distribution being non-thermal and this is not necessarily equivalent to the presence of RE. Many cases that show clear signs of RE have at the same time ξ < 0.065, suggesting that the plasma is to be considered predominantly thermal, though likely a small amount of RE are still detectable. As reported in section 3.1, a typical JET discharge with a low streaming parameter (ξ ≪ 0.065), though exhibiting small but measurable signs of start-up RE, would have a RE current that was only a few % of the total current.

However, figures 2–4, show several cases for which ξ starts to increase again and these are shown together in figure 12. Note that this figure also shows a comparable case for each device that shows normal thermalization. The higher value ξ (i.e. ξ > 0.1) at a larger current (later in the current ramp-up) is an indication that a larger fraction of the current is carried by RE. The streaming parameter, as given by equation (1), can be split into a thermal (ξ_TH) and a RE (ξ_RE) part, and, assuming that ξ_TH ≪ ξ, be approximated as:

$$\begin{align}\xi &= \frac{j}{{e{n_{\text{e}}}}}\frac{1}{{{v_{{\text{eTH}}}}}} = \frac{{{j_{{\text{TH}}}}}}{{e{n_{\text{e}}}{v_{{\text{eTH}}}}}} + {} \frac{{{j_{{\text{RE}}}}}}{{e{n_{\text{e}}}{v_{{\text{eTH}}}}}} = {\xi _{{\text{TH}}}} + {} \frac{{{n_{{\text{RE}}}}}}{{{n_{\text{e}}}}}\frac{c}{{{v_{{\text{eTH}}}}}} \nonumber\\ & \quad \sim {} \frac{{{n_{{\text{RE}}}}}}{{{n_{\text{e}}}}}\frac{c}{{{v_{{\text{eTH}}}}}}.\end{align} \tag{ 16 }$$

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Thus showing the streaming parameter becoming proportional to the fraction of RE. It is important to realize that the RE density n_RE≪ n_e, and even discharges with a current fully carried by RE (i.e. I_RE ∼ I), would have n_RE ∼ 10¹⁵ m⁻³ compared to a cold background thermal plasma with n_e ∼ 10¹⁸ m⁻³ [5].

The specific NSTX and JET cases show the typical higher ξ at plasma initiation that initially drops (thermalization), followed by a reversal at approximately a quarter of the current ramp-up, after which ξ increases steadily. Based on the available T_e data, although not always accurate, it is possible to estimate that all these cases with ξ > 0.1 also have a high fraction of the total current carried by RE. Thus the behaviour of these discharges is dominated by the RE and assumptions of for example Spitzer resistivity do not apply at this time anymore. The reason for this transition is that all these cases develop low values of n_e/j. This is purposely done for the NSTX cases, ramping down the density to generate RE for scientific purposes. Importantly, the plasma initiation and early ramp-up for these cases, ensure a quick decrease in the early ξ, hence these NSTX cases are likely having a short primary drive, creating a smaller seed than would be possible if the early density was kept lower. The two JET cases face a control error causing an unwanted decay of the density. The increase in I_RE also reduces the fraction of the thermal current and hence the Ohmic heating, usually yielding a collapse of the thermal plasma T_e, reminiscent of a burn-through failure during plasma initiation [5]. The very low values of n_e and T_e, under these circumstances, make it difficult to accurately determine ξ.

The lowering of n_e with respect to j, as is done for the NSTX cases, is generally known to be a scenario to enhance start-up RE. It is usually assumed that the reduction in n_e lowers E_c, possibly E_D and that this is sufficient to increase the RE generation. However, this process is less clear if one considered that lowering n_e leads to a higher T_e and thus a lower E as well. Thus, an increase in RE generation is not at all obvious, and especially not to take place on a time scale as shown here. A further point is that the role of RE losses or the RE confinement time in this process should not be underestimated. The balancing of RE generation and losses during the current ramp-up may be rather delicate. From the analysis in section 4.3, a rough indication of how the RE confinement scales from device to device was found. However, the RE loss process and how it scales in detail with tokamak discharge parameters, and thus how it may vary during the ramp-up, is not well understood. Another possibility is that the generation process itself is more complex than purely based on secondary generation given by equation (7), or possibly the seed created by the primary drive is larger than assumed here. The understanding of this process may require further study aided by self-consistent start-up simulations that include RE generation and losses.

Clearly, a dominating effect of RE on the discharge dynamics should be prevented. The formation of discharges with large values of ξ, and high fractions of I_RE, are prone to cause damage when they are terminated and thus should be avoided. But such cases are rather rare, while most devices can detect many cases that show signs of RE, only a handful of cases are found to develop into discharges that are dominated by RE. Also that the formation process of a full RE beam during the tokamak start-up is rather slow (as can be seen in figure 12) because of the low values of E/E_D (and E/E_c) during the development of these RE beams. For example, for the JET cases, this took about 1–2 s to complete. It is therefore perceived that this process is not a necessity, for start-up RE to be able to cause damage.