High density (≥6 × 10^{19} m^{−3}), low temperature (2–6 eV) helicon discharges in the Prototype Material Plasma Exposure eXperiment (Proto-MPEX) are analyzed with the coupled multifluid plasma, kinetic neutrals code B2.5-Eirene. The interpretative analyses are constrained by data from multiple diagnostics, including Langmuir probes, Mach probes, filterscopes, infrared TV system, Thomson scattering, and baratrons. The objectives of the transport simulations include: investigation of the effects of heating, fueling, and plasma production; pumping, and assumed radial transport models on the calculated density and temperature distributions; plasma flow profiles and power balance. The primary objective in this report is to investigate the effects of the radial transport model in full plasma (the entire length of the plasma column in Proto-MPEX) data-constrained simulations. Results from three assumed forms of the radial transport coefficients are presented, including spatially constant, radially decreasing, and Bohm (D,χ ∼ T_{e}/|B|). The results from each of the three transport coefficient sets agree qualitatively with the core (near axis) data. With the implicit T_{e} dependence, the Bohm coefficients tend to decrease as functions of radius, although not as strongly as the centrally peaked set. The axial variation in the Bohm coefficients is largely due to the axial structure of the magnetic field. The agreement of the simulations and the diagnostic data with the Bohm set indicates that transport in the plasma column of Proto-MPEX is dominated by Bohm diffusion.

## I. INTRODUCTION

A key objective of the Prototype Material Plasma Exposure eXperiment (Proto-MPEX)^{1} is the development of an intense plasma source for MPEX^{2} in which the plasma is produced by helicon waves, the electrons are heated by microwaves and Electron Bernstein Waves (EBW), and the ions are heated by Ion Cyclotron Resonance Frequency (ICRF) waves. The superconducting MPEX linear device in planning will provide steady state reactor relevant plasmas, as they are expected in a divertor of a reactor, for plasma–materials interaction (PMI) studies and the development of plasma facing components (PFCs).^{3} MPEX will be designed to handle a-priori neutron irradiated samples and expose them to high fluence plasmas for end-of-life studies of prototype PFCs. In order to achieve the divertor relevant plasma conditions, a high upstream heat flux has to be achieved and a high recycling regime has to be reached. Recycling of the majority gas, deuterium, at the target will lead to an increased electron density just in front of the target and a reduced electron temperature, just like in a high recycling divertor plasma. Previous simulations^{4} have shown that this regime could be obtained in MPEX with heat fluxes on the order of 20 MW/m^{2} and upstream densities of about 6 × 10^{19} m^{−3}. These simulations were carried out with many assumptions, such as absorbed heating power, plasma transport coefficients *D*, *χ _{e}*,

*χ*, recycling coefficients, and particle pumping. In these previous predictive simulations ad-hoc anomalous radial constant transport coefficients D,

_{i}*χ*, and

_{e}*χ*of 0.75, 1.5, and 1.5 m

_{i}^{2}/s were assumed. Together with the radially and axially localized electron and ion heat sources, the radial and axial transport coefficients determine largely the plasma profiles. In order to reduce the number of free variables, benchmarking of the code is of the essence and is the main motivation of this paper. The B2.5-Eirene simulations reported here are motivated by the need for code-model validation in support of the MPEX design activities. Previously B2.5-Eirene (or B2-Eirene) has been used to analyze plasma discharges in PSI-1,

^{5}MAGNUM-PSI,

^{6}PSI-2,

^{7}MAGPIE,

^{8}MPEX,

^{4}and Proto-MPEX.

^{9}Recently also other codes like Soledge2D coupled to Eirene

^{10}and LINDA

^{11}for modeling plasmas on Pilot-PSI and Gamma 10.

The focus of this work is related to the choice of the transport coefficients. Previous activities focused on the simulation of linear plasma simulators, which are in different transport regimes. For example, it turned out that the ions in the MAGPIE plasma are not magnetized, i.e., the ions are confined radially electrostatically. Electrostatic confinement is probably relevant for most low magnetic field linear plasma devices, whereas high field devices like Magnum-PSI and Proto-MPEX have magnetized ions.

Where possible, the analysis is constrained by the diagnostic data and otherwise guided by the results of those analyses. With data available from multiple locations throughout the plasma column, it is of interest to investigate different transport models to see which, if any, can describe the main features of the entire plasma from the target to the dump plate in various heating and pumping configurations. In the work reported here, three radial transport models (anomalous particle and energy transport coefficients having different radial behaviors, as well as Bohm transport models with radial and axial variations due to the dependency on T_{e} and B) are used in fitting the diagnostic data. The main research question addressed in this paper is: Can the transport be described by the Bohm model? If yes, this would significantly reduce the number of free parameters to fit the data. This will lead to time savings on the one hand for the interpretation of experimental results as well as allow much more straightforward extrapolation to MPEX conditions.

This paper is organized into five sections, the first of which is Sec. I. In Sec. II, a description of Proto-MPEX, its diagnostics and numerical tools used is given; in Sec. III, the assumed heating distributions and boundary conditions in the transport simulations are discussed. In Sec. IV, the three transport coefficient sets are introduced and discussed. In Sec. V, simulation results from each of the sets are given and compared with the diagnostic data. Concluding remarks are given in Sec. VI.

## II. DESCRIPTION OF PROTO-MPEX, NUMERICAL TOOLS AND DIAGNOSTICS

Proto-MPEX, the predecessor of MPEX, has demonstrated many of the required performance parameters. Proto-MPEX is a device making use of water-cooled copper coils allowing maximum magnetic fields of 2 T. The typical pulse duration of Proto-MPEX is between 0.15 s and 2 s. Experiments on Proto-MPEX have demonstrated high heat fluxes (>10 MW/m^{2}) and high particle fluxes (∼10^{24} m^{2}/s), albeit in low-density discharges. Recently, very high density (∼8 × 10^{19} m^{−3}) discharges,^{12} electron heating by Electron Bernstein Waves,^{13} and Ion Cyclotron Heating^{14} have demonstrated that reactor relevant plasmas at the target should be available with the addition of auxiliary electron and ion heating.

Analysis of the high density plasmas, produced by the helicon-only, reported in this work is performed with the coupled B2.5-Eirene^{15} code suite. The analysis of auxiliary heated discharges is not part of this analysis. B2.5 is a 2-D multifluid plasma code that solves conservation equations for the density and momentum of each charge state and the electron and ion energies. Eirene solves kinetic neutrals transport in arbitrary 3-D geometry with a Monte Carlo implementation and provides the source terms for the plasma conservation equations. Atomic physics data and data describing plasma and neutrals interactions with the walls (reflection, desorption, adsorption, and sputtering) are provided in files from ADAS,^{16} STRAHL,^{17} and TRIM.^{18} The atomic physics data used in this work is the standard set that is most often used in tokamak and linear device simulations and, due to limited justification for doing so, was not varied in the work reported here. This standard set includes the best available data for the plasma and neutrals processes that are important for modeling these experiments. The plasma-neutral and plasma-surface interactions are handled by the EIRENE code. Ion fluxes to the carbon dump and target are either recycled as molecules at 300 K or reflected as atoms. The particle and energy reflection coefficients are taken from the TRIM database.^{18,19} The neutral particles are followed in the plasma background provided by B2 until they change the state (e.g., ionization) or they are absorbed by a surface. Table I lists the atomic and molecular processes used in this work, with the rate coefficients taken from the AMJUEL and HYDHEL databases.^{19–21}

Reaction . | Description . |
---|---|

$D+e\u2192D++2e$ | Ionization |

$D+D+\u2192D+D+$ | Charge-exchange |

$D++e\u2192D+hv$ | Radiative and 3-body recombination |

$D2+e\u2192D2++2e$ | Nondissociative ionization |

$D2+e\u21922D+e$ | Dissociation |

$D2+e\u2192D+D++2e$ | Dissociative ionization |

$D2+D+\u2192D2+D+$ | Elastic collision |

Reaction . | Description . |
---|---|

$D+e\u2192D++2e$ | Ionization |

$D+D+\u2192D+D+$ | Charge-exchange |

$D++e\u2192D+hv$ | Radiative and 3-body recombination |

$D2+e\u2192D2++2e$ | Nondissociative ionization |

$D2+e\u21922D+e$ | Dissociation |

$D2+e\u2192D+D++2e$ | Dissociative ionization |

$D2+D+\u2192D2+D+$ | Elastic collision |

The reflection, adsorption, and desorption rates depend upon the incident angle, energy, and species of the impacting projectile as well as the surface material (C, Fe, Mo, etc.). Likewise, the plasma-neutral interaction rates depend upon the plasma and neutral species, the plasma density and temperature, and the neutral velocity distribution. All these dependencies are calculated self-consistently with B2-Eirene.

A schematic diagram of Proto-MPEX in Fig. 1 shows the twelve coils, numbered 1–12 from the dump end to the target end, that generate the magnetic field. Also shown in Fig. 1 is the axial plot of |B| in an optimum field configuration for helicon operation. The positions of Double Langmuir Probe (DLP) and Mach probe insertion points are located at spool pieces between coils. References 22 and 24 describe theoretically the effect of RF fields on the symmetric DLP. These studies show that the “time-averaged” I-V characteristic of the symmetric DLP over an RF cycle can be correctly analyzed using the theory of the undisturbed DLP. By “undisturbed” we mean in the absence of RF fields. This has the consequence that no RF compensation circuitry is needed to correctly extract the electron temperature from the time-averaged I-V characteristic of the symmetric DLP. This observation has been confirmed experimentally as shown in Fig. 12 of Ref. 23.

As per the experimental setup in Ref. 22, we used a symmetric Double Langmuir Probe (DLP) and a 1:1: transformer to galvanically decouple the DLP from ground; as a result, the DLP was electrically floating relative to the plasma. As per Ref. 23, we chose an appropriate probe tip diameter so that for conditions typical of Proto-MPEX the Debye length is much smaller than the probe radius and therefore we avoid RF induced sheath expansion effects. As per Refs. 22, 23, and 24, we used the standard DLP theory to analyze the time-averaged signals to extract n_{e} and T_{e}. The DLPs used in this study were swept at 200 Hz using a 1:1 magnetically coupled power supply providing a triangular waveform of −60 to 60 V. The current collecting tips were made from a Tungsten wire 0.25 mm in diameter and 2 mm in length. The entire probe shaft is shielded with a stainless-steel tube and enclosed in a ceramic tube to take the heat load from the plasma.

The gas fueling valve for the discharges analyzed here is noted on the diagram and is located 30 cm downstream from the helicon. The Thomson scattering location used is that at spool piece 11.5 (between coils 11 and 12). The target plate is at coil 12 and the dump plate is at the opposite end of the vacuum chamber. Only helicon heating and plasma production (no Electron Cyclotron Heating or Ion Cyclotron Heating) are active in these discharges.

## III. BOUNDARY CONDITIONS AND PLASMA HEATING DISTRIBUTIONS

In the plasma flow simulation along field lines to a solid surface, a sheath is assumed to form between the last grid cell of the plasma and the surface. In fluid codes like B2.5, the kinetic sheath physics is replaced by fluid equations containing sheath transmission coefficients that describe the kinetic processes that limit the particle and energy flow to the surface. The Bohm criterion is prescribed in B2.5 to obtain a monotonic potential drop across the sheath with the Mach number constrained to be unity so that the particle flow will be at least sonic at the sheath entrance. The form of the electron and ion heat fluxes to the end plates and associated sheath heat transmission coefficients used at both ends of the grid for all of the simulations reported here are discussed in Refs. 13 and 25. Recent measurements of the plasma flow in Proto-MPEX^{26} confirm Mach numbers of 1 close to the target downstream and a stagnation point where the Mach number is close to zero in the region of plasma production, the helicon antenna. Toward the dump plate Mach numbers of 0.5 were measured. In Ref. 26 these values were compared to B2-Eirene simulations with a radially constant diffusion coefficient.

The boundary conditions at the outer boundary of the grid are specified by average radial scale lengths of the density and temperature profiles. (A strong axial dependence of the radial scale lengths at the outer boundary of the measured density and temperature profiles is seen in Figs. 8 and 9, but only axially constant scale length boundary conditions are available in the code.) The spatially constant and radially decreasing transport models are estimated to require λ_{T} = 1.5 cm and λ_{n} = 0.75 cm. (With these two transport models, the focus was on fitting the near axis core plasma data.) For the Bohm model, smaller scale lengths (λ_{T} = 1.0 cm and λ_{n} = 0.5 cm) were chosen as more appropriate when edge heating leads to edge peaking of the density and temperature profiles and radial gradients can be steep (see Figs. 8 and 9). Zero shear in the parallel velocity is prescribed as the momentum equation boundary condition at the outer boundary of the plasma grid. Since unity recycling coefficient is prescribed on the outer boundary, plasma that reaches that boundary is recycled as neutrals into the plasma column with reduced energy. At the center of the plasma column (r = 0), it is assumed that the radial gradients vanish, and the corresponding particle, momentum, and energy fluxes are equal to zero. It is evident from Figs. 8 and 9 that at several axial diagnostic locations, the radial profiles are not centered on the axis. For these locations, the calculated profile fits will be circular and thus fit the data only in an average sense. Hence, the emphasis mentioned above for fitting the on-axis data. It should be emphasized that both the boundary conditions and the assumed particle and energy transport coefficients are important in getting the best fit to the diagnostic data. In the work reported here, only minor adjustments in the original assumed forms of the boundary conditions were necessary and those were primarily at the outer radial boundary of the plasma grid. Fits to the data were largely obtained by adjusting the magnitudes of the particle and energy transport coefficients for the spatially constant and Bohm coefficient sets and both the magnitude and radial form of the centrally peaked set. The spatial-axial and radial-behaviors of the Bohm coefficients are determined by the behavior of the electron temperature and the magnetic field. Only the magnitudes of particle diffusivity are varied for the Bohm set with the ratio of heat to particle diffusivities set to 2.0.

The (axially compressed) physical mesh used in the analyses reported here is shown in Fig. 2. The three pumping locations, the gas injection port, the helicon, the skimmer disk, and the radial extent of the target and dump plates are noted. The axial grid lines are coincident with the magnetic field lines and the radial grid lines are chosen to be perpendicular to the axis (r = 0). The radial extent of the mesh is limited by the helicon antenna structure. The purpose of the skimmer is to limit the conductance of neutrals to the central cell, where a small neutral density is needed for effective electron cyclotron resonance heating (ECH).

The helicon heating distribution of the electrons is shown in Fig. 3. No ion cyclotron heating (ICH), electron cyclotron resonance heating (ECH) or electron Bernstein wave heating (EBW) is used. The helicon heating distribution shown is based on the assumption that heating occurs near the axial location of the helicon. The radial form factor shown in Fig. 3 right hand panel is based on the assumption that, depending on the plasma density, the higher density helicon mode heating or the lower density Trivelpiece-Gould (TG) mode^{27} heating or both can effectively produce plasma and heat the discharge. Since the TG mode cannot propagate at densities greater than ∼10^{18}, in the higher density discharges analyzed here, the core plasma is heated by the helicon mode and the TG mode mainly heats the low-density edge plasma. This TG heating can lead to edge peaking of the plasma radial profiles. Even though some edge peaking of the absorbed power distribution is included, as in Fig. 3, it does not necessarily lead to edge peaking in the B2.5-Eirene density and temperature profiles due to effects of radial transport. Much stronger edge power deposition will, however, be evident with edge peaking in the simulation results. These assumptions are supported by full wave simulations of the helicon wave physics^{28} using the finite element analysis software COMSOL Multiphysics and measurements of the transition from an edge heating dominated profile by TG-modes to a more core heated helicon mode plasma.^{29} The results of this modeling show the central heating of the helicon normal modes and the edge heating due to TG-modes. IR measurements in Ref. 29 show the power deposition profiles before the TG-modes and after the transition. The radial transport modeling presented in this paper is assuming radial and axial heating profiles. It should be stated that these heating profiles are not calculated in a self-consistent manner, where *ab-initio* calculations of RF wave coupling are included in a whole-device modeling approach.

Except for the pumping ports, the vacuum vessel walls are assumed to be nonabsorbing with unity recycling coefficients. Gas puff and desorbed species are assumed to leave the wall or end plate in a cosine distribution at a constant energy of 0.026 eV (assuming wall temperature = 300 K).

Pumping in the discharges analyzed here is performed at three axial locations. (See Ref. 16 for a more complete discussion of pumping experiments and the choice of pumping surfaces in the simulations.) The effects of pumping are included in the calculations by imposing an albedo or recycling coefficient for neutrals on surfaces at or near the locations of the turbo pumps. Typically, the recycling coefficients and pumping surface areas in the simulations are: at the ballast tank surface 0.8 (area = 290.6 cm^{2}), at the expansion tank location 0.984 (area = 301 cm^{2}), and at the central cell 0.99653 (area = 8786 cm^{2}). In the spatially constant transport coefficients case, the recycling coefficient at the expansion tank location was increased to 0.993 in order to give a better fit to the density data near the dump plate.

## IV. TRANSPORT MODELS

In this section, the choice of diffusive transport coefficients (D, χ_{e}, and χ_{i}) and general features of the transport in the simulations are discussed. Three diffusion coefficient sets are chosen for the analysis. The parameters of each set are determined by varying the model parameters in multiple runs until a “best fit” is obtained. Depending upon the diffusion coefficient model, the best fit agreement with the experimental data maybe only qualitative. (It should be emphasized that the choice of different boundary conditions often requires adjustment of the transport coefficients in order to get the best fit to the diagnostic data.) The spatially constant set is denoted by “constant” in the figures and the values are D = 0.5 m^{2}/s, χ_{e} = χ_{i} = 1.0 m^{2}/s. (see Fig. 4). In general, if the scale length boundary conditions used on the radial boundary are increased (decreased), the D and χ values should be increased (decreased) in order to retain the same radial fluxes. The first is spatially constant and adjusted to fit the data with the particular boundary conditions that are assumed.

In the second transport coefficient set, the D and χ are peaked on-axis (and denoted by “peaked” in the figures) and decrease to small values at the outer boundary of the grid. This choice limits the radial fluxes out of the grid and forces more of the plasma fluxes to the target and dump plates. Also, limiting the ion flux and retaining more of the ions at the edge partially compensates for the ionization source that is present there but not included in the simulation. It is shown in Sec. V that this characterization of the transport coefficient set gives the best overall agreement with the data.

The third set assumes Bohm diffusion (D = η_{D}T_{e}/16|B|)^{30,31} with T_{e} in electron volt and B in Tesla, and is labeled “Bohm” in the figures. In the work reported here, η_{D} = 0.5 and χ_{e} and χ_{i} have the same form with η_{χ} = 1.0. The structure of the Bohm coefficients, seen in Fig. 5, is largely determined by |B| and to a lesser extent by the axial variation of T_{e}. It is noted that the large peak in D and χ at the axial position of the helicon (due to small |B| at that location) results in correspondingly large radial fluxes to the helicon window structure and recycling or reflection of neutrals back into the plasma. This possibly results in a significant power sink. This loss of power is indirectly being taken into account by applying less heating power in the B2.5-Eirene simulations than in the experiment. The absorbed heating power in the B2.5-Eirene simulations is 16 kW, whereas in the experiments the coupled heating power is 100 kW and the absorbed heating power is in the range of 12–47 kW.^{32} The B2.5-Eirene heat flux to the target is up to 0.7 MW/m^{−2}, close to experiments which show about 0.9 MW/m^{−2} (Ref. 32).

MPEX will rely on conduction limited parallel transport to achieve the needed plasma parameters in front of the target. It is therefore instructive to examine the components of the parallel fluxes in these high density discharges in Proto-MPEX. In the particle and energy balance summaries, B2.5-Eirene does not characterize the components as convective or conductive, but rather based on their origin. For example, in Fig. 6 the energy fluxes are fluxes of kinetic energy, ion thermal energy, electron thermal energy, and potential (ionization) energy. Usually, the largest of these is the ionization energy which resides in the neutrals upon recombination in the volume or in the surface. From T_{e} and its axial gradient and the ion flux, the convective and conductive heat fluxes are computed on the axis and shown in Fig. 7. Without additional heating, the parallel heat transport from the Bohm set simulation is dominantly convective. This is not too surprising and calls for future work to analyze strongly electron heated plasmas.

## V. COMPARISON OF SIMULATION RESULTS AND DATA

B2.5-Eirene full plasma simulations are compared to radial profiles of electron density and temperature measured with Double Langmuir probes as well as Thomson Scattering at multiple axial locations along the plasma column, and axial distribution of D_{α} radial line-integrated data from filterscopes. Previously^{26} axial and radial profiles of Mach probe measurements for helicon plasma in Proto-MPEX were already compared to B2-Eirene modeling and hence are not repeated here. The radial and axial profiles of the Mach probe data agree qualitatively well with the B2-Eirene simulations within the measurement limitations. In Figs. 8 and 9, the results for the three radial diffusive transport models at four axial locations are shown. The data are not azimuthally symmetric so comparison with the data should be focused on the near axis region and the 2D calculated radial profiles viewed as an average of the in-out (with respect to the axis) density and temperature measurements. The peaked and Bohm models tend to give the best agreement between modeling and the experimental density and temperature radial profiles. In particular, the density profiles seem to be best fit with the Bohm model. The Bohm model describes the high density at spool 1.5 the best. Both peaked and Bohm models can describe the electron density profiles reasonable downstream toward the target. The constant diffusion profile is not able to reconstruct the density profile close to the target. But most importantly, the Bohm model describes the electron density at the upstream part between the helicon antenna and dump tank. The electron temperatures are fit well with the peaked and Bohm model. Although it seems that the Bohm model is better in describing the upstream part toward the dump tank, it shows consistently higher temperatures downstream. The reason why the Bohm model does lead to a better comparison of the modeling with experimental data just upstream of the helicon antenna is most likely related to the fact that the magnetic field has a minimum there and the diffusion coefficient is much higher at that location than in the peaked profile. Several of the experimentally measured radial profiles show evidence of edge heating but the calculations do not include a strong edge heating term that would be required to reproduce the data at those locations.

In Figs. 10 and 11, the results for the three radial diffusive transport models are compared to the probe density and temperature measurements on-axis. The best overall agreement is with the peaked case and almost as well are the Bohm profiles. With the Bohm diffusion model the calculated density is higher at the gas valve location and the electron temperature is greater than the measurements near the target. The density from the constant case fits quite well except for the strong decrease as the target is approached. Comparison of the peaked and Bohm model simulations with chord integrated D_{α} filterscope measurements in Fig. 12 also shows very good agreement over the entire plasma column.

Quantities that are of particular interest for optimization of ECH and ICH, as well as heating and plasma production with the helicon, are the neutral densities and pressures in the heating zones. Axial profiles of radially averaged neutral atomic and molecular densities are shown in Fig. 13 for the Bohm diffusion coefficients case. Both the atomic and molecular density curves show increases due to the gas puff. Strong recycling from the helicon structure gives a peak in the atomic density at the helicon which could lead to enhanced charge exchange losses. Graphs of molecular pressure at the radial edge of the plasma in Fig. 14 also show an uptick at the gas valve. The edge pressure for the Bohm case is significantly higher than that for the peaked case, possibly due to suppressed molecular dissociation in the plasma edge.

An estimate for the Bohm case of the total (axially integrated) radial heat and particle fluxes is given in Fig. 15. Approximately twice as much ion flux is escaping (and recycling) radially than is fueled via the gas valve in the simulation. For the same case, almost 3 kW crosses the radial boundary, most of which does not return.

The transport coefficients found here are different from those used in predictions for MPEX (D = 0.75 m^{2}/s, χ_{e} = χ_{i} = 1.5 m^{2}/s).^{4} Future work needs to take into account the electron heating and the ion heating. After benchmarking the B2.5-Eirene model to the additional heated discharges, an updated prediction of the plasma parameters in front of the target for MPEX can be performed, which should give critical information for the design of MPEX.

## VI. SUMMARY AND CONCLUDING REMARKS

Plasma transport in high density helicon discharges in Proto-MPEX has been analyzed with the B2.5-Eirene code. Extensive diagnostic data sets, including data from axial arrays of Langmuir probes, Mach probes, filterscopes, infrared TV system (IRTV), Thomson scattering, and baratrons (capacitive manometers) constrain the analyses. With absorbed power distributions localized at the axial location of the helicon, the analysis is focused on the effects of different radial anomalous transport coefficient sets (D, χ_{e}, and χ_{i}) as well as Bohm-like transport models, which have axial and radial varying transport coefficients, in determining the power and particle fluxes that reach the target for PMI studies. While the present study is limited to a single magnetic field configuration, input power (∼100 kW) and heating-plasma production with the helicon-only, it is demonstrated that the plasma distributions in the high density helicon discharges are describable by Bohm diffusion and anomalous peaked transport models, the parameters of which have been adjusted to fit the data. The Bohm model also predicts large radial fluxes of particles and energy in the region of the helicon when the magnetic field is optimal for helicon operation.

Although the modeling with the ad-hoc peaked diffusion coefficients gives overall a reasonable fit to the experimental data, it is inferior to the Bohm-like transport model which can describe the electron density and electron temperature profiles better in regions with a low magnetic field. Overall the Bohm diffusion coefficients used in B2.5-Eirene describe the experimental data rather well. This is particularly satisfactory, since in the future extrapolations with a more physics-based approach to the transport can be used, which should improve predictions for MPEX.^{1}

With the transport models used here, it is demonstrated that these discharges are convection dominated. Auxiliary heating with the ECH and ICH systems will likely be required to enter the conduction dominated regime. Further work is required to benchmark the modeling against ECH and ICH heated discharges to validate the predicted conduction limited transport regime needed for MPEX.

## ACKNOWLEDGMENTS

This work was authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).