Experimental and numerical modeling of plasma start-up assisted by electron drift injection on J-TEXT

Start-up is one of the critical phases for tokamak discharge. The electron drift injection (EDI) system has been developed on J-TEXT for start-up studies. A breakdown experiment with EDI-assisted start-up has been conducted, which verified the effect of pre-ionization by EDI to achieve start-up at a lower ohmic field voltage. A zero-dimensional (0D) model has been developed to explain the effect of EDI quantitatively. The comparison between the experiment and simulation verified the credibility of this model. Based on this model, a comparison between pure ohmic heating start-up and EDI-assisted start-up was presented, showing that EDI improved ionization, causing a lower delay to the peak of hydrogen ionization and radiation losses and a smoother rise in the electron and ion energy. This result quantitatively verified the pre-ionization effect of EDI on start-up . The effects of injecting different currents and electron energy were investigated. A better pre-ionization effect was realized by increasing the injected current, which can be a reference for the upgrading of the EDI system.


Introduction
The start-up is a crucial process for tokamak discharge. It consists of breakdown, burn-through and ramp-up [1]. In the breakdown process, pre-fill is heavily ionized due to the Townsend avalanche by the toroidal electric field, while in the burnthrough process impurities are fully ionized so that the electron temperature can reach 100 eV [2]. However, the start-up process draws little attention, except for spherical tokamaks, because there are already successful start-ups for all currently running conventional tokamaks. For a sizeable superconducting tokamak, like ITER, things are different. Start-up becomes a serious issue because of limitations on the toroidal electrical field, the thick vacuum vessel wall, gas puffing far away from the vacuum vessel, and so on [3]. Hence, there are still many issues that need to be further studied.
For research on the start-up, the most usual method that can be used for pre-ionization is electron cyclotron heating, as mentioned in some of the works above. But we still hope that there are other methods that can be an alternative choice for assisting start-ups. For example, coaxial helicity injection should be a good choice for the spherical torus start-up. With this motivation, we developed an electron drift injection (EDI) system on J-TEXT [55]. The commissioning of the EDI system was carried out to demonstrate the feasibility of the EDI system in injecting electrons into the inner vessel. The application of the EDI system reduced the breakdown delay and loop voltage and expanded the limitation of pre-fill pressure. These works on J-TEXT verified the feasibility and validity of J-TEXT.
This paper focuses on analyzing the results systematically, with a newly developed model and with an expansion of our previous work [55]. Typical experimental results will be shown. The simulation was also carried out. Considering the actual discharge physics meaning and giving some hypotheses to describe the effect of the EDI system on start-up, we developed the 0D model, which makes it possible to combine the experiment with simulation. The simulation results clarified the contribution of the EDI to start-up. A comparison of the effect after injecting different currents and electron energy showed that better pre-ionization can be achieved by increasing the injected current. This result can also be used as a reference for EDI system upgrading.
This paper consists of five sections. It is organized as follows: a brief introduction to the EDI system and experimental setup is in section 2. Section 3 illustrates the start-up model. Section 4 gives the results and analysis both in the experiments and simulations. Lastly, there is a summary and discussion in section 5.

Experimental setup and the EDI system
In this section, the experimental setup will be introduced first. Then the EDI system will be described.

Experimental setup
The J-TEXT tokamak is a traditional conventional ironcore tokamak with a major radius R 0 = 1.05 m, minor radius a = 25-29 cm with a movable titanium carbide-coated graphite limiter. The typical J-TEXT discharge in the limiter configuration occurs with a toroidal field B t of ∼2.0 T, a plasma current I p of ∼200 kA, a pulse length of 800 ms, a plasma density n e of 1 − 7 × 10 19 m −3 and an electron temperature T e of ∼1 keV [56].
The primary diagnostics for this experiment are the photodiode array (PDA), electron cyclotron emission (ECE) system, far-infrared (FIR) interferometer system, vacuum gauge and some basic diagnostics. Figure 1 shows the distribution of these diagnostics and the EDI system from a top view. The PDA array, which measures the H α radiation, consists of 17 channels installed at the bottom of port 4. The EDI system, which will be described in the following section, is installed at the top of port 4. The ECE system can measure relative electron temperature. The FIR interferometer system provides information on plasma density. From the vacuum gauge, we can get the pre-fill pressure (or neutral pressure) within the vacuum vessel.
The ohmic field of the J-TEXT tokamak consists of a premagnetizing rectifier and capacitor, an ionization capacitor and four general capacitors, as shown in figure 2. The premagnetizing rectifier works first, causing a reverse current in the ohmic coil. When the pre-magnetizing capacitor is charged to a preset voltage, it will be discharged to the pre-magnetizing rectifier, making the latter turn off. Then the ionization capacitor is triggered. Furthermore, an induced toroidal field will cause an avalanche effect in the neutral gas within the vacuum vessel. The collision between free electrons and hydrogen happens so that the initial plasma is generated. The capacitor C 1  and subsequent capacitors are applied depending on the amplitude of the H α signal. We define when the discharge control system triggers the pre-magnetizing capacitor as time zero.
Usually, we set the voltage of the ionization capacitor at 1600 V, corresponding to a toroidal breakdown electric field of 5.21 V m −1 , to achieve reliable breakdown. The minimum breakdown voltage for a successful ohmic start-up is about 800 V, corresponding to a toroidal breakdown electric field of 2.15 V m −1 . The lower the voltage of the ionization capacitor, the lower the induced toroidal electric field. Pure ohmic heating cannot successfully discharge at the lower toroidal electric field. However, ohmic heating start-up can succeed with EDI assistance, which can verify the effect of EDI. That is the strategy in this experiment. In reality, the EDI system was applied from −50 ms to 0 ms before applying the ionization capacitor voltage of 700 V. Besides the injection time, the main parameters used to describe this system are the injec-tion current and the energy of injected electrons. As measured by experiments, the injection current and energy of injected electrons are about 30 mA and 100 eV, respectively.

Description of the EDI system
The EDI system is based on the principle of electron drift. Figure 3(a) shows the schematic diagram of the EDI system. When discharging, a high toroidal magnetic field of several Teslas is generated around the tokamak. Suppose that we establish a radial reversed electrical field: electrons in this area will drift into the vessel by ⃗ E × ⃗ B. Electrons can be generated by heating the cathode gun to about 1300 K, corresponding to a major power of 60 W (12 V and 5A), while a high electric field of 5 × 10 5 V m −1 can be achieved by applying a high voltage on two stainless steel plates. The total power to operate the EDI system is about 62 W. The structure diagram of the EDI system  (1): Electrons will also gain a magnetic gradient drift, namely, Electrons can also gain a rate of curvature drift, namely, Compared with these velocities, the major velocity is the electric field drift. Based on such principles, we developed the EDI system and carried out test experiments [55]. Later, the EDI system, mainly the cathode gun, was upgraded to improve its performance. The size of the cathode having the capability to emit electrons is s = π × (0.5) 2 cm 2 . The cathode can form a current of about 0.79 A but, due to the collision with a negative concave plate, the actual injected current was reduced to about 0.3 A. This paper uses a more modest value of 0.03 A in the model to describe the injected current. Another critical parameter is the energy of injected electrons. The simulation results show that the energy of injected electrons has a relatively wide distribution, as shown in figure 4. Hence, we adopted a mid-value of 100 eV to finish the simulation of typical discharge. Our team carried out further work based on this system, such as putting the EDI system into a low loop voltage start-up experiment. The related results will be presented later in this paper.

0D model of EDI
Based on the typical model developed by Lloyd et al [34] and referring to the work by Hada et al [57] and Kim et al [44], we developed a 0D model to describe the role of EDI during the start-up. The start-up processes is divided into the pre-ionization stage and inductive discharge stage, as shown in figure 5. The pre-ionization stage lasts from −50 ms to 0 ms, in which the EDI system works, and there is no inductive field. The inductive discharge begins at 0 ms. The toroidal field is induced by the changing flux caused by changing current in the central coils. The two stages have different particle and energy balances, as shown in tables 1 and 2. The two stages will be discussed as follows.

Pre-ionization stage assisted by EDI
At this time, there is no collisional equilibration. So we give three assumptions first at this stage.
• There is no collision equilibration, and the ion energy remains constant. • The energy of injected electrons is always constant as it is does not affect much on ionization.   Parameter Pre-ionization Inductive discharge ne Generation n inj ionization (major) a n inj ionization (minor) Electron ionization (minor) Electron ionization (major) Loss Transport loss Transport loss τp=0.015 s b τp=0.03 s b a Ionization caused by injected electron. b τp is the particle confinement time.
• The ionization of impurities can be ignored due to low electron energy.
Based on these assumptions, this stage can be described by four equations consisting of four basic parameters: electron energy (T e , unit in eV), electron density (n e , unit in m −3 ), injected electron density (n inj , unit in m −3 ) and the neutral density (n 0 ). The four equations are equations (4), (5), (6) and (7) [34,44,[57][58][59]: dn e dt = n 0 n e S − n e τ p + S 1 n 0 n inj (5) Parameter Pre-ionization Inductive discharge neTe a Gain b P EDI ; P OH = 0 P OH ; P EDI = 0 Loss c P D (major), P brem (major), P e con , P dr ,Perr P D (major), P equi (major),P brem , P e con (major), P dr , Perr No equilibration P equi Loss Pcx, P i con a ne is the electron density, Te is the electron energy. b The input energy includes EDI, PEDI, and ohmic heating, P OH . c The electron energy loss includes the ionization and radiation PD, equilibration loss P equi , bremsstrahlung loss P brem , transport loss P e con , drift loss P dr and error field loss Perr. d n i is the ion density, T i is the ion energy.
Here is a description of these equations.

Injection electron density balance equation.
As shown in equation (4), the first term on the right side is injected electrons, which causes the density of injected electrons to increase. The particle number can be expressed by where I inj is the injection current from the injected electrons. Other terms n, s, and v are the injected electron density, sectional area of injected electron beam and the velocity of the injected electron, respectively. All the terms in this text with a subscript of 'inj' are related to the injected electrons. V v is the vacuum vessel volume. The energy of injected electrons is much higher than that of electrons in the vessel. The process of thermalization, rather than ionization, will dominate the plasma behavior. Conservation of energy also should be considered under the assumption of constant T inj . A coefficient of η 1 is introduced to deal with this process and can be roughly estimated as 0.05 by analyzing the overall energy conservation during the pre-ionization.
The second term on the right side of the equation (4): the electrons in the vacuum vessel are gradually lost due to poor confinement. τ inj is the confinement time of injected electrons. Considering the drift motion, parallel transport and Bohm diffusion, we give it a value of 0.005 s. In this model, the electron density n e is different from injected electron density n inj .

Electron density balance equation.
As described by equation (5), the change in electron density is mainly affected by two factors: ionization and loss. The first term on the right side of equation (5) represents the contribution of ionization collisions between electrons and the neutral. V n is the neutral volume. It can be calculated from equation (8) [34]: where V p is the plasma volume, which can be calculated by V p = 2π R 0 · π a 2 . R 0 is the major radius, and a is the minor radius. V n /V p takes into account the influence of the neutral shielding effect. The mean free path, λ i , is introduced [34]: where v 0 is the velocity of hydrogen atoms. n 0 in equation (5) is the neutral (hydrogen) density. S is the ratio coefficient of electron ionization. It can be calculated by [34]: The second term on the right-hand side of equation (5) characterizes the influence of particle losses on density. In this term, τ p is the particle confinement time. The final term shows the contribution of injected electrons by the EDI system to increasing electron density. S 1 is the rate coefficient for electron ionization (per atom) caused by injected electrons, namely, T e in equation (10) which is the value of injected electron energy T inj .

Electron energy density balance equation.
The electron energy is mainly determined by equation (6). The left side of equation (6) describes the rate of change of electron energy density. The terms of P EDI , P Hion + P Hrad , P brem , P e con , P err and P dr represent the power density of EDI power, hydrogen ionization and radiation, bremsstrahlung loss, convective transport loss and the energy loss caused by error field and drift, respectively. More details are shown in the following text. Two common terms, ohmic heating power and the equilibration, are not included in equation (6). Ohmic heating power (P OH ) is the primary energy input for the conventional start-up. However, at the pre-ionization stage, there is no ohmic heating. The EDI power term, the assisted energy input, becomes the primary energy input. We assume that there is no collision equilibration because the large fraction of electrons is at low energy, and the density is also low. The following part shows the calculation of these terms.
The total power introduced into the system by the EDI system can be characterized as the product of the total number of injected particles and the energy contained in a single particle. The number of particles flowing to the vacuum vessel per unit time is The meanings of related parameters have been presented before. The energy of particles flowing into a vacuum vessel is T inj . Due to the temperature conversion, the power density introduced by the EDI system can be characterized as equation (11). Considering the energy distribution, we add a coefficient of η 2 into this expression. The value of this coefficient is 0.95 in this model.
Regardless of impurities, the losses related to electron energy density include neutral ionization and radiation energy, P Hion + P Hrad , corresponding to ionization and radiation energy density. They can be converted to ionization and radiation energy by multiplying by a factor of V p . The next several terms are similar in this respect: balance collision (P equi ), bremsstrahlung (P brem ), electron transport (P e con ), drift (P dr ) and error field (P err ).
In equation (6), the neutral ionization and radiation energy loss are defined as [34]: The total power loss per ionization is [34]: Regardless of impurities, the bremsstrahlung loss per unit volume is [34]: The transport losses by electron can be described by [58]: In equation (15), τ e is the electron energy confinement time. For simplicity, τ p and τ e take the same value of 0.015 s during pre-ionization [34,59].
At the start-up stage, the error field can affect the effective connection length, which means the movement distance for particles along the field line from ionization to collide with the wall. It can be given by [57]: In equation (16), V T is the thermal velocity of electrons, and I c is the critical plasma current necessary to cancel the error field component, which can be given by The particles can be lost due to gradient drift and curvature drift, which is calculated by [57]: 3.1.4. Neutral density balance equation. The neutral density is determined by equation (7). The pre-ionization effect is small, not negligible. Hence, the change in neutral density is still included. The equations (4)- (7) can qualitatively describe the contribution of EDI to pre-ionization.

Electron energy density balance equation.
As described by equation (18), it is unnecessary to take P EDI into consideration after the EDI system is turned off. However, the terms of ohmic heating power and collision equilibration should be taken into consideration, which are the apparent differences between equation (18) and equation (6). The ohmic heating power is the main input energy. The ohmic heating power density can be described by [34]: where R p is the plasma resistance. It can be determined by [34]: where ln Λ is the Coulomb logarithm and Z eff is the effective charge.
The energy exchange between electrons and ions is mainly achieved through collision equilibration. In this equation, the power density of collision equilibration is given by [34]: where n H is the hydrogen ion density, n I is the impurity density, A I is the impurity ion mass number and summation is over impurity species. When plasma experiences the process of burn-through, the impurities will be ionized by electrons, emitting strong line radiation. The radiation is given by equation (27) [57]: The balance of ion energy density can be described by equation (19). The prefill gas in J-TEXT is hydrogen. The following formula can calculate the charge exchange power loss of hydrogen atoms [34]: In this equation, T 0 is the background temperature. The charge exchange ratio coefficient of each atom can be calculated from equation (29), This formula is obtained by fitting [60]. The final term of the equation is ion transport loss, and its expression is [58]: where τ i is the ion energy confinement time in this equation. The closed flux surface begins forming during inductive discharge, enhancing the confinement. Hence, we give the confinement time as τ e = τ i = τ p = 0.03 s [34,57,59]. V is the loop voltage in the tokamak discharge. L is the plasma inductance, which is regarded as a constant. The calculation method is as follows [34]: For a flat current distribution, we take the internal inductance l i ≈ 0.5. For the J-TEXT tokamak, the plasma inductance can be calculated as 2.33 × 10 −6 H.

Electron density balance equation.
Equation (21) describes the balance of electrons. The electrons and injected electrons can ionize the neutral to generate electrons, as described by the first term and third term on the right-hand side of equation (21). The ionized electrons can also be lost by transport.

Neutral density balance equation.
The balance of neutral density is described by equation (22). A brief model was adopted in this work. The density change rate of the neut-ral is opposite to that of the electron density. The influence of impurities and other factors has been ignored.

Injected electron density balance equation.
The balance of injected electron density can be described by equation (23). Considering the parallel and perpendicular transport [44], we give the injected electrons a different confinement time (τ inj ) of 1 ms, which is different from the confinement time during pre-ionization.
The loop voltage or toroidal field is a critical parameter in tokamak discharge and the primary energy source of inductive discharge, which significantly impacts parameters such as plasma current. The loop voltage in the classic model adopts a constant value, but during the start-up phase on J-TEXT, the loop voltage changes significantly. For example, during the breakdown, the loop voltage spike can reach 34 V for conventional discharge in the J-TEXT tokamak. However, the loop voltage is stable at about 2 V in the flat-top phase. Therefore, it is not appropriate to adopt a fixed loop voltage to simulate. So we are motivated to introduce the experimental loop voltage into the simulation.
In experiments, the loop voltage usually has a minus peak value caused by the reversed voltage to turn off the thyristor in a pre-magnetized power supply discharge circuit. In signal processing, the negative voltage is ignored. Moreover, similar processing has been applied to other signals simultaneously to keep signals consistent. We adopted the ode15s solver in MATLAB to solve these stiff differential equations. Ode15s is a variable step solver. Likely, there is no acquisition data for loop voltage at particular times. The linear interpolation method is adopted to solve this problem.

Initial conditions
The initial electron energy and ion energy value are at room temperature (300 K). The initial value of the plasma current is 0 A. The pressure at the initial moment of ohmic heating is 2.5 ∼ 3 mPa (refer to figure 6), which is converted into a density of 1.2 ∼ 1.44 × 10 18 m −3 . Considering that the vacuum vessel is far away from the vacuum gauge and the vacuum gauge itself has a measurement error of about 30%, it is estimated that the actual pre-fill pressure in the vacuum vessel may be 50% higher than the measured value. Hence, we give an initial neutral density of 1.9 × 10 18 m −3 . J-TEXT discharges with a carbon limiter. Based on the diagnostic data, the oxygen and carbon densities are considered to be 0.5% and 5%, respectively.
A pretty low ionization rate is given to allow comparison between pure ohmic heating and EDI-assisted start-up. The initial electron density is set to 1.5 × 10 12 m −3 in this simulation. The injected electron density at the initial time is 0 m −3 with EDI-assisted start-up. The EDI-assisted start-up is divided into two stages, which have been described earlier.
The final value of the EDI pre-ionization process is taken as the initial value of the inductive discharge stage. Due to the continuous action of the vacuum pump, the prefill pressure in the vacuum vessel continues to drop. Here it is assumed that the pressure remains unchanged. The primary purpose of this process is to reduce the complexity of the model and, at the same time, more clearly compare the effect of EDI-assisted start-up. Namely, neutral density at −50 ms with EDI-assisted start-up is the same as the initial density of pre-fill pressure at 0 ms with the pure ohmic start-up.
The time of the ode15s solver must be greater than 0, but we turned the EDI system on at −50 ms and started the premagnetizing capacitor at 0 ms in the experiment. To ensure the smooth calculation of the simulation, we offset the time axis of the entire discharge by 50 ms. We start applying EDI to assist start-up at 0 s, turn off EDI at 50 ms, and then start inductive discharge in the simulation.

Results and analysis
The research on EDI-assisted start-ups was from 2009. Based on those results, the related simulation work was carried out.
Here are the typical experimental results.

Typical EDI-assisted start-up experiment on J-TEXT
The low loop voltage experiment has been conducted on the J-TEXT tokamak. Figure 6 shows the temporal evolution of some parameters in three different cases. Case 2 and case 3 are ohmic heating start-ups, while case 1 is the EDI-assisted start-up (just pre-ionization). Case 1 and case 2 have the same ionization capacitor voltage (700 V), which is lower than the voltage of the ionization capacitor (800 V) applied in case 3. A comparison between case 2 and case 3 indicates that the minimum successful breakdown loop voltage for pure ohmic heating is about 16 V (case 3). On the other hand, the application of EDI before inductive discharge successfully expands this voltage to 14.2 V. The pre-fill pressure at the beginning of the start-up is similar. It can be considered that the pre-fill pressures are equal. After a high toroidal electric field is applied (the loop voltage is about 14 V) is applied, the EDI-assisted start-up discharge produces H α radiation with an amplitude about twice that of a pure ohmic start-up. The subsequent H α radiation from EDI assistance is almost equal to that of a pure ohmic start-up. There is nearly no obvious H α radiation after 0.015 s for pure ohmic discharge. After the successful breakdown, the plasma density with EDI-assisted start-up ramps up rapidly to the order of average line density of 10 19 m −3 . This growth trend is similar to that of case 3 but not case 2. In case 1, after apparent plasma density appears, the plasma current also starts to ramp up and finally maintains a flat-top state after reaching the preset value of 150 kA.
Start-up is successful with EDI assistance, generating the desired plasma current and density, rather than a failed discharge (case 2) for pure ohmic heating start-up under a group of similar discharge parameters. This indicates that EDI assistance expands the operation limitation for ohmic heating start-ups, making a difference in the start-up process. An explanation for the above phenomenon is that the higher energy electrons injected by EDI (100 eV) promote the ionization of neutral gas or provide a certain amount of power at the beginning of discharge, which improves the plasma start-up.
However, since no significant increase in plasma density is observed from the HCN interferometer, the injected electrons may not contribute much to the rise in the initial plasma density. At a constant ionization capacitor voltage, if the injected electrons have a higher energy, theoretically, the toroidal field required for breakdown will be appropriately reduced. However, it is also impossible to distinguish a significant loop voltage drop from the discharge waveform. Therefore, it is difficult to determine whether the number of injected electrons dominates the power at the beginning of the discharge or whether the energy of the injected electrons contributes to the shot. This is also a motivation to solve this question by simulation.

Comparison between experiment and simulation
Based on the discharge model described above and the experimental loop voltage of case 1 presented in figure 6, we have obtained simulation results for the EDI-assisted start-up. Figure 7 shows the comparison between the simulated results and the experimental results. It can be seen from the figure that the simulation plasma current is similar to the experiment, the trend of electron energy is similar, and the electron density is similar in the initial stage. Note that the experimental density is obtained by converting the multichannel HCN density to a uniform density. However, there is a significant difference in the latter. The final value (at 0.1 s) of simulated electron density is 1.89 × 10 18 m −3 while the experimental value is 9.6 × 10 18 m −3 . The reason is that some experimental effects are not included in the model. When the neutral particles in the plasma section are fully ionized, there is no remaining gas available for ionization. Besides that, plasma equilibrium can be another factor affecting plasma density, especially the experimental core density. The simulated electron energy is shown here, while the experimental electron energy is not presented here because there is not enough experimental diagnostics data to provide an uniform electron energy during start-up.
Compared with the experimental result, although the simulation results are not perfect, they are reasonable at the initial stage and in the order of magnitude. In this model, the toroidal electric field and the plasma inductance can strongly affect the plasma current. In the discharge, the plasma inductance changes relatively slowly. If the given initial value is reasonably accurate, the simulation results can reach a higher agreement with the experimental results. More accurate results require a higher dimensional code and more physical details.
Another common problem is a specific measurement error, whether a diagnostic or a measuring instrument. When the simulation result is close to the experimental result, we cannot confirm the experimental data, or the simulation result is more convincing. However, we can ensure that the simulation results are similar to the experimental results, indicating that the simulation can be a good reference and that the model is reasonable.

Analysis of EDI-assisted start-up from simulation
Based on the above judgment, we analyze the main contribution of EDI to the start-up process from a simulation perspective.
We simulated pure ohmic start-up and EDI-assisted startup. In the case of pre-ionization, the electron energy increased from 0.026 eV to 2.13 eV. The ion energy and the neutral density are constant. Electron density grows from 1.5 × 10 12 m −3 to 7.2 × 10 15 m −3 . The simulation results of essential parameters for the pure ohmic heating start-up and EDI-assisted start-up at the inductive stage are shown in figure 8. Due to the increase in initial parameters, the electron density in the early stage of discharge is apparently higher than that of pure ohmic heating, and it tends to be consistent in the later stage. Another apparent difference is the electron energy. There is an apparent peak in electron energy at the early stage of ohmic heating start-up. Nevertheless, the electron energy grows gradually for EDI-assisted start-ups. These differences can be explained by the fact that when the input ohmic heating power is equal, the total energy (n e T e ) is almost the same, leading to a higher electron density corresponding to low electron energy. Given enough time (0.7 ms), electron density rises, and the input energy will be distributed to all electrons through collisions. From t = 0.0507 ms, the parameters of EDI-assisted start-up are similar to those of pure ohmic heating.
The simulation results of some power density terms are shown in figure 9. It can be seen that some critical power density terms, such as P OH , P D and P equi , grow faster and are higher for EDI-assisted start-up than for ohmic heating start-up at the initial stage (0.05-0.0505 s). However, the differences are very small. Some parameters of ohmic heating start-up are a little higher than those of EDI-assisted start-up around the time of 0.051 s. The temporal evolution of power density with EDI assistance is presented in figure 10. Some minimal power density terms, for example, drift loss, are not presented in this figure.
The reason for these phenomena can be explained as follows. For the start-up assisted by EDI, the plasma develops a little faster, corresponding to the earlier appearance of P D and quicker development of P OH and P equi . After 1 ms of inductive discharge, there are also differences in P OH and P D . This can be explained as follows: the neutral densities are equal, and the total ionization and radiation can be seen as the same. EDI has extra ionization and radiation before the inductive discharge. Hence, it requires less ionization and radiation power in the inductive discharge. Plasma assisted by EDI can develop a little faster so that it can reach its final state a little earlier. The little differences in plasma current cause the differences in P OH . After 2 ms, the differences in all parameters are negligible, indicating that EDI can play a role in start-up, but its contribution is still weak. The comparison of power between the process of EDI pre-ionization and inductive discharge  (figure 10) also supports this idea. Optimizing the EDI parameters might improve the performance: we next carry out a simulation, scanning injected electron energy and current, to investigate this.

Effect of injected currents on start-up
Based on this model, we simulated the conditions of different injected currents (0.03, 0.3, 0.15 and 0.003 A) for the pre-ionization process, which are shown in figure 11. When injected current is increased, the plasma current increases, as shown in figure 12. The explanation is as follows. On increasing the injected current, the injected electron density increases(figure 12 (d)), leading to an increase in ionization (the quantitative analysis corresponds to equation (5)). As the population of particles is fixed, the neutral density decreases while the electron density increases. However, despite a 100fold change in the injected current, the variation between the largest and the smallest plasma current does not exceed 5% within the first 2 ms. Increasing injected current contributes less to the electron energy and ion energy. However, it can significantly increase initial electron density for inductive discharge. The largest initial electron density and the smallest electron density are 7.14 × 10 16 m −3 and 7.234 × 10 14 m −3 , respectively. As neutral density is much larger (about 100 times or more) than electron density, neutral density changes little. A high injected current corresponds to an increased initial injected density. Then all the injected currents shown in figure 11 decay quickly and tend to reach the same final state. This change is due to poor confinement. The differences in electron energy are also apparent in the first 1 ms. It is observed that higher electron energy corresponds to a low electron density. The reason has been explained before. This phenomenon indicates that higher injected current contributes mostly to the increase in electron density rather than electron energy.   Figure 13 shows the temporal evolution of related power densities. The similar final states in all parameters, including power density in figure 13 and basic parameters in figure 11, show that EDI will play a role in the early stage of a start-up but not affect the discharge parameters by much. The reason is that the input EDI power is much smaller than the ohmic heating power, and it also does not play a role when the ohmic heating starts working.   Figure 14 shows the evolution of basic parameters after trying different injected electron energies. It is easily seen from figure 14 that when the injected electron energy increases from the original 100 eV to 1 keV, the difference is tiny. Only when the injected electron energy is increased to 10 keV can we see an apparent difference from the original case. The ion energy grows quickly at first. Then all the ion energies become closer. Finally, the ion energy in the case of injected electron energy Figure 15. Evolution of related power densities: ohmic power density (a), equilibration power density (b), ionization and radiation power density (c), ion transport power density (d), electron transport power density (e) and charge-exchange power density ( f ) after improving the injected electron energy. of 10 keV is lower than that in the other cases. On increasing injected electron energy from 100 eV to 1 keV, the initial electron density changes from 7.2 × 10 15 m −3 to 5.17 × 10 16 m −3 , while the electron energy changes from 2.1 eV to 2.3 eV. Even on increasing the electron energy to 10 keV, the electron energy increases to only 2.4 eV. It is assumed that at 10 keV some assumptions of the model (i.e. no impurity ionization by injected electrons) are still valid. However, an energy of two orders of magnitude greater that the experimental case should be treated with more caution. Figure 15 shows the evolution of related power densities on increasing electron energy. From the evolution of power density, it can be easily seen that there are only slight differences in all power densities when the injected electron energy does not exceed 1 keV. When the injected electron energy reaches 10 keV, there exist apparent differences in all power densities.

Effect of injected electron energy on start-up
The further analysis of these phenomena is as follows. Improving injected electron energy contributes to the increase of electron energy and density. However, the largest initial electron energy (2.4 eV) is still low. In contrast, the changes in electron energy are more apparent. Increasing the injected electron energy to 10 keV leads to a significant increase and widens the gap in all related parameters when compared to the other three cases with different injected electron energies. The increased electron energy promotes the equilibration between electrons and ions, increasing ion energy. However, regardless of the energy of the injected electrons used for ionization, the electron energy is still low, resulting in a high plasma resistance and a rather small plasma current. The obvious differences in P equi and P D support this analysis.
Increasing injected electron energy and current contributes to increasing the initial electron density and energy. However, the effect on electron energy is weak. Improving electron density will have a more prominent effect on start-up. Combined with figures 11 and 14, it can also be confirmed that the main effect of EDI in improving the start-up is to increase the electron density. When increasing the injected electron energy and injected current by the same order of magnitude, the effect is more apparent in the case of increasing injected current, which also indicates that improving injected current should be the development direction of the EDI system.

Discussion and conclusion
This paper presented the EDI experiment and simulation on J-TEXT. For a typical discharge, EDI assistance has been shown to have the capability to expand the operation range of a tokamak, for example, by decreasing the voltage requirement for the ohmic field coil. Considering the physical meaning, we introduced related terms and developed a 0D EDIassisted start-up model. Comparison between experimental results and simulation shows that this model is coherent, while it is not perfect in some aspects. The simulation results for pure ohmic heating start-up and EDI-assisted start-up explained the effect of EDI pre-ionization on start-up quantitatively. Injecting different currents and electron energy was investigated. Increasing the injected current had a more apparent effect than higher electron energy injection. But all these EDI parameters had little effect on the final result at flat-top for a successful discharge, indicating that the capability of EDI is limited. The effect of EDI may be not be as good as the usual electron cyclotron heating but it may be a good supplement to the methods of assisting start-ups, in particular having a cost advantage. We further analyzed the effect of increasing injected current and electron energy theoretically, and these results will be verified in our future experiments.