VeloAlpha System Code (VSC) Overview

• VSC is a unified computational framework that performs zero-dimensional power-balance analysis for five distinct magnetic confinement configurations.
• The system integrates configuration-specific geometry, profile weights, and confinement closures with a shared solver interface to ensure consistency and traceability.
• It supports both single-point evaluations and 2D plasma operating contour scans, enabling rapid assessment and comparative analysis in early-stage fusion reactor design.

Searching arXiv for the VSC paper and closely related fusion system-code context. The VeloAlpha System Code (VSC) is a computational framework for zero-dimensional fusion power-balance studies across five magnetic-confinement configurations—tokamaks, magnetic mirrors, field-reversed configurations (FRCs), dipoles, and stellarators—within a common power-balance formulation that connects fusion production, charged-particle deposition, radiation, transport loss, external heating, and fusion gain while preserving configuration-specific geometry, profile weights, confinement model, and operating constraints (Wang et al., 13 Jul 2026). The same solver interface supports both single-point calculations and two-dimensional plasma operating contour (POPCON) scans, producing fusion and heating powers, gain, radiation and transport losses, geometry quantities, and configuration-specific validity indicators. In this formulation, VSC is oriented toward rapid assessment and comparative analysis of candidate fusion reactor concepts during the early design stage, with emphasis on transparency, traceability, and rapid parameter-space exploration rather than replacement of higher-fidelity 1.5D/2D/3D tools (Wang et al., 13 Jul 2026).

1. Scope and supported magnetic-confinement configurations

VSC supports five device classes, each with specialized geometric and physical models: tokamaks, magnetic mirrors, field-reversed configurations, dipoles, and stellarators (Wang et al., 13 Jul 2026). The framework is unified at the level of power accounting, but each branch retains its own closure logic and operating diagnostics. This division is central to the code’s design: the shared solver interface standardizes comparisons, while branch-specific models preserve the differences that determine accessible operating space.

For tokamaks, VSC includes multiple analytic and equilibrium-imported geometries and allows either predictive or manual confinement closure. For magnetic mirrors, the code models a central cell plus throat contraction, includes multi-channel loss models, and incorporates end-loss and ambipolar potential physics. For FRCs, the implementation is based on rigid-rotor equilibrium, finite-length separatrix, and pressure-balance closure. For dipoles, VSC provides point-dipole or finite-current-loop options with shell-based profiles and a parametric confinement treatment. For stellarators, the supported geometry descriptions include near-axis analytic, boundary Fourier, and imported VMEC/DESC geometries, together with ISS04 and Sudo closures (Wang et al., 13 Jul 2026).

This suggests that VSC is structured not as a single reduced model applied indiscriminately to all concepts, but as a common accounting backbone wrapped around branch-specific geometry and confinement assumptions. A plausible implication is that comparisons produced by VSC are most meaningful when interpreted as comparisons of reduced-order model closures under a common accounting convention, rather than as geometry-agnostic performance rankings.

2. Shared zero-dimensional power-balance formulation

At the core of VSC is a volume-integrated 0-D power-accounting equation. The formulation relates fusion production, charged-particle deposition, radiative losses, transport losses, external heating, and fusion gain in a consistent bookkeeping structure across all supported configurations (Wang et al., 13 Jul 2026).

Fusion production is written as

$$P_{fus} = \frac{E_{fus}}{1+\delta_{12}} n_{1,0} n_{2,0} \Phi_{fus} V_p$$

where $E_{fus}$ is the released energy per reaction, $n_{1,0}$ and $n_{2,0}$ are the core reactant densities, $\Phi_{fus}$ is the profile-weighted reactivity, and $V_p$ is the plasma volume (Wang et al., 13 Jul 2026). The framework explicitly handles dilution, impurity fractions, and related species accounting.

The external heating requirement is defined by the balance

$$P_{heat} = P_{trans} + P_{brem} + P_{cycl} + P_{line} - P_{charged,dep}$$

with fusion gain

$Q_{fus} = \frac{P_{fus}}{P_{heat}}$

where $P_{trans}$ is transport loss, $P_{brem}$ is bremsstrahlung loss, $E_{fus}$0 is cyclotron or synchrotron radiation loss, $E_{fus}$1 is impurity line and recombination radiation, and $E_{fus}$2 is the deposited energy from charged fusion products after configuration-specific deposition losses (Wang et al., 13 Jul 2026).

The significance of this shared accounting lies in the fact that a single solver contract can expose how different assumptions about density, temperature, magnetic field, geometry, and confinement move a concept through or out of a feasible operating window. Because the code returns identical top-level power-balance quantities for all branches, differences between configurations can be traced back to branch-specific geometry, profile weights, and confinement closure rather than to incompatible output definitions.

3. Modeling of fusion production, radiation, deposition, and transport

VSC treats fusion production using branch-specific application of Bosch-Hale fits for reactivity $E_{fus}$3, while explicitly capturing impurity and He-ash dilution, impurity $E_{fus}$4, species mass, and reactant fractions (Wang et al., 13 Jul 2026). The effective charge is written as

$E_{fus}$5

which enters the species-resolved radiative accounting (Wang et al., 13 Jul 2026).

The energy released by fusion is split into neutron and charged channels according to

$E_{fus}$6

and the deposited charged-particle power is reduced in open configurations when losses occur; for mirrors, the deposition fraction $E_{fus}$7 can be reduced due to the loss cone (Wang et al., 13 Jul 2026).

For bremsstrahlung, VSC uses a species-resolved, profile-integrated treatment employing the Xie Gaunt-factor fit:

$E_{fus}$8

with the total bremsstrahlung power obtained from volume integration, $E_{fus}$9 (Wang et al., 13 Jul 2026). Line and recombination radiation can be included as an optional impurity contribution through

$n_{1,0}$0

to avoid double-counting the electron-ion bremsstrahlung component (Wang et al., 13 Jul 2026). Cyclotron or synchrotron radiation is treated with branch-specific models, including Trubnikov/Albajar for tokamaks and numerical $n_{1,0}$1-moments for mirrors, while explicit loss times may also be user-specified (Wang et al., 13 Jul 2026).

Transport loss is expressed as

$n_{1,0}$2

where $n_{1,0}$3 is the thermal energy and $n_{1,0}$4 is the configuration-specific energy confinement time (Wang et al., 13 Jul 2026). The closure for $n_{1,0}$5 varies by branch. Tokamaks and stellarators support either predictive confinement scalings or prescribed $n_{1,0}$6. Mirrors assemble confinement from Pastukhov, gas-dynamic, and radial times, including ambipolar potential and regime flags. FRCs use empirical LSX-scaling, with particle lifetime acting as a $n_{1,0}$7 proxy. Dipoles have no predictive closure and require user-supplied $n_{1,0}$8 (Wang et al., 13 Jul 2026).

VSC also treats two-temperature effects explicitly through ion-electron energy exchange:

$n_{1,0}$9

with charged fusion product energy channeled accordingly (Wang et al., 13 Jul 2026). This detail matters because it allows the shared 0-D framework to distinguish electron-side and ion-side heating pathways rather than collapsing all thermal channels into a single-temperature approximation.

4. Configuration-specific geometry, confinement closure, and validity logic

Although VSC is unified at the solver level, each configuration retains its own geometry and radial coordinate, profile weights, confinement model, and operating constraints (Wang et al., 13 Jul 2026). These choices determine how the common power-balance skeleton is instantiated.

For tokamaks and stellarators, VSC uses a volume-radius description with either analytic boundary models or imported equilibria. Tokamaks support analytic (elliptic, Miller), Cerfon-Freidberg, and imported equilibrium geometries, while stellarators support near-axis, boundary Fourier, and imported representations (Wang et al., 13 Jul 2026). Tokamak confinement can be predictive or manual, with redline diagnostics such as Greenwald density, $n_{2,0}$0-related limits, $n_{2,0}$1, $n_{2,0}$2, $n_{2,0}$3, and L-H thresholds reported; stellarators analogously expose Sudo, $n_{2,0}$4, and $n_{2,0}$5 indicators (Wang et al., 13 Jul 2026).

For magnetic mirrors, geometry is modeled as a self-similar cylinder with an analytic volume plus sin-throat contraction, and confinement is built from the assembled Pastukhov/gas-dynamic/radial times. Mirror-specific diagnostics include $n_{2,0}$6 limit, Pastukhov regime, and loss-cone alpha fraction (Wang et al., 13 Jul 2026).

For FRCs, VSC adopts rigid-rotor geometry with pressure-balance fixed density and Ma-Xie separatrix modeling. The confinement model uses empirical LSX scaling or manual $n_{2,0}$7, while validity logic reports quantities such as $n_{2,0}$8 for tilt, $n_{2,0}$9, and flux diagnostics (Wang et al., 13 Jul 2026).

For dipoles, the geometry is represented through point/finite ring shell models with shell volume (flux) profiles. Confinement is parametric, requiring an input $\Phi_{fus}$0, and redlines include shell $\Phi_{fus}$1 and $\Phi_{fus}$2 (Wang et al., 13 Jul 2026).

A plausible implication is that VSC’s comparative value depends strongly on how transparently these closures are selected and reported. Because the framework returns configuration-specific validity indicators, it is designed not merely to compute a power balance, but to contextualize that balance within each concept’s native operational constraints.

5. Solver interface, outputs, and POPCON workflow

VSC exposes a common workflow through single-point evaluation via run_case and two-dimensional parameter scans via scan2d (Wang et al., 13 Jul 2026). Both branches use the same accounting skeleton but invoke different geometry, profile, transport, and validity routines depending on configuration.

The computational workflow comprises five stated steps: input normalization/validation for the selected configuration; geometry and profile weights generation; power balance solve; diagnostic calculation; and outputs and masks, which surface fusion power, gain, heating, and window validity (Wang et al., 13 Jul 2026). This sequence gives the framework a traceable structure in which preprocessing, physical closure, and postprocessing are separated.

The solver contract is described as

$\Phi_{fus}$3

where the outputs include fusion power, required heating, gain, radiative and transport losses, plasma volume, plasma surface, wall area, and configuration-specific diagnostics or redlines (Wang et al., 13 Jul 2026). Geometry and profile weights, including moments such as $\Phi_{fus}$4, can also be returned when requested.

In POPCON mode, VSC performs 2D scans over user-selected variables, usually density $\Phi_{fus}$5 temperature, and evaluates the core model at each grid point (Wang et al., 13 Jul 2026). Invalid points or redline violations are recorded and masked. The scan then applies default or user-specified operating region masks, such as $\Phi_{fus}$6 or $\Phi_{fus}$7, and returns maps of fusion power, heating requirement, gain, losses, geometry metrics, and validity indicators (Wang et al., 13 Jul 2026).

The ability to use the same solver interface for both single operating points and POPCON maps is consequential. It means that operating-window analysis and point-design analysis share the same underlying bookkeeping and closure logic, reducing ambiguity about whether a contour plot and a point calculation are based on different internal assumptions.

6. Interpretation, applications, and relation to broader reduced-order fusion studies

VSC is presented as a unified, transparent platform for early-phase, cross-topology fusion device evaluation, making it possible to study how assumptions about density, temperature, magnetic field, confinement, and geometry shape the accessible operating space of different fusion concepts within one traceable framework (Wang et al., 13 Jul 2026). The stated applications include rapid scans and comparisons, traceable publication outputs, identification of the required combination of geometry, field, density, temperature, and assumed confinement for candidate devices, and generation of branch-specific diagnostics relevant to interpretation and design (Wang et al., 13 Jul 2026).

The code is explicitly positioned for early-stage reactor design and comparative analysis. It is not described as a substitute for higher-dimensional integrated modeling. That distinction is methodologically important: VSC’s reduced-order nature allows rapid exploration, but its outputs depend on the validity of configuration-specific closures and assumed profile weights. This suggests that VSC is most effective as a front-end screening and hypothesis-formulation tool, to be followed by more detailed engineering or physics studies once a promising operating window has been identified.

The framework also includes a web interface at https://hub.veloalpha.cn/vsc/ supporting preset selection, parameter editing, configuration switching, geometry/profile browsers, and POPCON visualization tabs, with launches of scans and display of default and user-custom operating masks (Wang et al., 13 Jul 2026). A plausible implication is that VSC aims to make reduced-order, cross-topology comparison reproducible and inspectable not only at the level of equations but also at the level of user workflow.

7. Misconceptions, limits, and methodological significance

A common misconception would be to read VSC as a claim that all magnetic-confinement concepts can be evaluated under a single universal physics model. The underlying description does not support that interpretation. Instead, VSC uses a common power-balance formulation while allowing each configuration to retain its own geometry, profile weights, confinement model, and operating constraints (Wang et al., 13 Jul 2026). The framework is unified in accounting, not homogenized in physics closure.

Another potential misconception is that a 0-D system code can establish definitive reactor performance. The stated purpose is more limited and more precise: rapid assessment and comparative analysis of candidate fusion reactor concepts during the early design stage (Wang et al., 13 Jul 2026). The framework’s value lies in surfacing sensitivities and operating windows under explicit assumptions. Its limitations follow from reduced dimensionality, branch-specific closure assumptions, and the fact that operational validity is represented through configuration-specific validity indicators rather than through full spatially resolved dynamics.

Methodologically, VSC occupies a distinctive place by combining reduced-order physics models with a unified computational platform across concepts that are often analyzed in separate modeling traditions (Wang et al., 13 Jul 2026). This commonality in interface and output structure makes direct comparison possible without erasing the underlying differences in topology and confinement. In that sense, VSC’s central contribution is not merely a collection of zero-dimensional models, but a traceable comparative framework in which common outputs and concept-specific redlines coexist.