A Three-Module Grouped XRAM Topology for Electromagnetic Railgun Drive: Topology Comparison, Parameter Optimization, and Mechanism Verification

Abstract

Inductive pulsed power remains attractive for demanding electromagnetic acceleration systems because of its high-current capability and rapid discharge capability. Within this class, XRAM is especially appealing because it combines series charging with parallel discharging of storage inductors. Under high-energy conditions, however, the conventional all-parallel XRAM topology suffers from concentrated blocking-voltage stress on the total output switch and limited effectiveness in transferring stored current to the representative railgun load considered in this work. To address these issues, this paper proposes a three-module grouped XRAM topology and examines its output behavior, parameter dependence, and commutation mechanism. Baseline comparison results show that the grouped arrangement establishes the load-driving path earlier and redistributes device stress more favorably. Its advantage is retained when both topologies are individually optimized with respect to the triggering threshold, indicating that the grouped topology offers a more effective route for high-current electromagnetic acceleration drive through earlier commutation establishment and more effective current transfer.

1. Introduction

Electromagnetic railguns are often studied as demanding high-current electromagnetic acceleration platforms because of their ability to accelerate payloads to very high speeds through direct electromagnetic force [1,2]. The same class of pulsed-power and current–transfer problems is relevant to broader civilian applications, including hypervelocity material-strength testing, extreme impact-loading studies, engineering rock breaking, and other high-load electromechanical acceleration systems. Within such systems, the pulsed power supply is not a peripheral component but rather the functional core: the choice of circuit topology and the associated parameter settings jointly govern how quickly current builds up in the barrel, how effectively the stored energy reaches the load, and what voltage burdens the key switching devices must withstand.

A substantial body of published work has examined parameter selection and launch-scenario modeling for railgun systems [3,4], alongside engineering demonstrations conducted at both experimental and system scales [5,6]. In terms of energy storage, capacitor banks represent the historically dominant approach and continue to see deployment in practical pulsed-power installations [7,8]. Inductive storage, by contrast, offers a different set of trade-offs: the inductor-based supply is inherently better suited to sustaining high current into a low-impedance load, and it affords greater flexibility in shaping the output pulse [9,10]. As shown in Figure 1, the two approaches differ at a fundamental circuit level in both the primary storage element and the manner in which that energy is routed to the load.

The broader context of inductive electromagnetic launch has also been explored from launch-system and pulsed-power-system perspectives [11,12], and several overviews confirm that inductive pulsed power continues to attract interest as a high-performance launch architecture [13,14]. More recent assessments reinforce this view, pointing to the ongoing engineering relevance of advanced pulsed-power circuit concepts for electromagnetic acceleration applications, including material testing and other high-load industrial scenarios [15,16].

Within the inductive pulsed power family, XRAM occupies a distinctive position by exploiting series charging and parallel discharging of energy-storage inductors simultaneously [17,18]. Figure 2 first summarizes the complete XRAM topology used for conceptual explanation, while the representative equivalent current-flow schematics in Figure 3 isolate the two basic switching states. In the left panel of Figure 3, the charging switches are closed and the discharge switches remain open; so, the branch inductors accumulate magnetic energy while the load path is effectively inactive. In the right panel, the charging switches are opened and the discharge switches are closed; so, the branch currents are redirected and summed at the load. The key technical challenge is therefore commutation: the charging current must be interrupted and the stored inductor energy must be redirected toward the load. To accomplish this with high-current semiconductor devices, inverse current commutation with semiconductor (ICCOS) has been introduced into XRAM generators [18]. Under high-energy-output conditions, however, the conventional all-parallel XRAM arrangement remains vulnerable to two coupled problems: excessive blocking-voltage concentration on the total output switch, and less favorable establishment of the load-driving path, both of which reduce how effectively the stored inductor current reaches the railgun load.

To address these two issues simultaneously, this paper proposes a three-module grouped XRAM topology. While the conventional directly paralleled 12-module structure treats all modules equivalently, the proposed design partitions them into three structurally symmetric submodule groups. This reorganization preserves the high-current-output characteristic that makes XRAM attractive for electromagnetic acceleration applications while introducing group-level control over the energy-release rhythm and commutation sequence, thereby providing a structural route to redistribute output-switch stress and advance the formation of the main load pulse. The topology’s performance, however, does not follow from structure alone; it depends on the coupled interaction of the main-storage precharge voltage, the reverse-capacitor precharge voltages, and the commutation triggering threshold. Characterizing these interactions therefore requires more than a handful of operating-point simulations.

The railgun load used in the present study should therefore be understood as a representative and highly demanding electromagnetic launch load through which the pulsed-power topology can be assessed. The circuit-level conclusions pursued here concern how grouped XRAM architecture affects current transfer, device stress redistribution, and load-access timing, and these issues remain relevant to broader electromagnetic launch and acceleration applications even beyond the specific railgun context.

Most existing studies on multistage pulsed power supplies have emphasized output enhancement and device-voltage balancing [10,16]. More recent work has extended this line of research to parameter optimization [19,20]. What remains less clear is how topology choice and parameter optimization interact. In particular, once the over-voltage limit is relaxed and each topology is allowed to optimize its own triggering threshold, it is still necessary to ask whether a new topology retains a genuine structural advantage.

This question is central to the grouped topology proposed here. We therefore examine three issues in sequence: whether its timing and stress advantages remain when the two topologies are compared under equal initial stored energy and comparable voltage levels, which parameters set the performance ceiling and which mainly serve as commutation-matching variables, and whether the remaining advantage after relaxing the over-voltage boundary comes from a higher current peak or from a more favorable commutation and current–transfer process.

The contribution of this work is threefold. First, it introduces a three-module grouped XRAM topology and compares it systematically with the conventional 12-module all-parallel topology under equal initial stored energy and comparable voltage levels. Second, it formulates an optimization problem with maximum armature speed as the main objective and with device over-voltage and thyristor turn-off feasibility as constraints, and then uses one-dimensional sweeps, two-dimensional coupling maps, and local four-dimensional refinement to identify the dominant parameter effects and the feasible high-performance region. Third, it employs a trigger-threshold-optimized comparison to show that the performance gain of the grouped topology is structural rather than incidental, and that it is linked mainly to earlier commutation establishment and more effective transfer of internal storage current to the load.

To position the proposed topology more explicitly with respect to representative modular XRAM structures reported in the literature,

Table 1. Comparison between the proposed grouped topology and representative modular XRAM structures reported in the literature.

Reference/	Stages	Module	Load-Drive	Grouped	Stress	Threshold
Topology		Organization	Focus	Design	Analysis	Optimization
Liebfried et al. [17]	4	Single-level multistage XRAM	Yes	No	No	No
Dedié et al. [18]	8	Single-level ICCOS-XRAM	No	No	No	No
Dedié et al. [16]	20	Single-level toroidal XRAM	No	No	No	No
This work	12	Three-group partitioned XRAM	Yes	Yes	Yes	Yes

summarizes the main architectural and analytical differences. Existing XRAM studies have demonstrated single-level multistage structures with different stage counts and semiconductor commutation arrangements [16,17,18]. By contrast, the present work introduces an explicit group-level partition within a fixed 12-module XRAM system, and combines this structural modification with stress-redistribution analysis, threshold-optimized comparison, and a dedicated scalability discussion.

The rest of this paper is organized as follows: Section 2 introduces the modeling framework, the ICCOS operating principle, and the evaluation indices. Section 3 presents the baseline comparison, system-level loss estimation, parameter-optimization results, and the group-count scalability discussion. Section 4 uses the trigger-threshold-optimized comparison together with current-integral and transfer-ratio metrics to interpret the origin of the performance gap. Section 5 concludes this paper.

2. Materials and Methods

This section introduces the modeling framework and evaluation basis used throughout this paper. Section 2.1 describes the grouped-topology structure and the parameter reduction strategy. Section 2.2 presents the railgun load model. Section 2.3 explains the operating principle of the ICCOS module and the triggering criterion. Section 2.4 summarizes the simulation model and the comparison principles. Section 2.5 defines the optimization objective and constraints, and Section 2.6 introduces the performance indices used in the subsequent results and discussion.

2.1. Topology Description and Parameter Reduction

The topology under investigation partitions twelve XRAM modules into three structurally identical submodule groups. Within each group, a main energy-storage branch, a reverse-commutation branch, a set of multistage inductors, and a thyristor switching network work in concert to build and redirect the stored current. All three groups feed into the railgun load through a shared total output switch, with the actual energy delivery occurring during the commutation phase. For comparison purposes, a conventional directly paralleled 12-module XRAM topology is considered alongside the proposed design; it retains the same total stage count but foregoes any group-level partitioning.

Figure 4 contrasts the two circuit arrangements: the proposed design organizes its modules into groups, whereas the conventional topology simply places all twelve modules in parallel with no intermediate hierarchy. The single-stage ICCOS commutation unit discussed later represents one embedded branch-level ICCOS cell from Figure 4a, and it is this structural difference that ultimately drives the distinctions in commutation timing, stress distribution, and load-driving behavior observed later.

The three-fold group symmetry of the proposed topology makes it natural to impose a group-constrained parameterization, which reduces the dimensionality of the optimization problem without discarding the physically meaningful differences between branches. Concretely, the three main-storage voltages are tied together as $U_S=U_{S,1}=U_{S,2}=U_{S,3}$ so that a single variable $U_S$ characterizes the energy level of all three groups simultaneously.

A finer distinction is drawn for the reverse-commutation capacitors, because the leading branch within each group carries a disproportionate share of the initial blocking duty and plays a more active role in establishing commutation. Accordingly, the precharge voltages of the three leading-branch capacitors are collected into a single variable $U_{C,a}$, while those of the remaining nine branches are represented by $U_{C,b}$: $U_{C,1}=U_{C,5}=U_{C,9}=U_{C,a}$ and $U_{C,2}=U_{C,3}=U_{C,4}=U_{C,6}=U_{C,7}=U_{C,8}=U_{C,10}=U_{C,11}=U_{C,12}=U_{C,b}$. This two-tier grouping honors the functional asymmetry between leading and non-leading branches while compressing the parameter space to four optimization variables: $U_S$, $U_{C,a}$, $U_{C,b}$, and $U_{\mathrm{th}}$.

2.2. Railgun Load Modeling

To describe the dynamic coupling between the pulsed power supply and the electromagnetic railgun load, a system-level electrical–mechanical equivalent model is adopted [21,22]. Related dynamic and inductance-gradient modeling approaches have also been reported in [23,24]. In the present work, the railgun load is represented through a position-dependent inductive-resistive branch together with a simplified armature-motion model so that the dominant current–transfer and acceleration effects can be retained without introducing a full field-circuit co-simulation framework. The corresponding equivalent structure is summarized in Figure 5.

$$u_{\mathrm{load}}=\left(R^{\prime }x+R_v\left(v\right)\right)i_{\mathrm{load}}+L\left(x\right){\displaystyle \frac{d{i}_{\mathrm{load}}}{dt}}+i_{\mathrm{load}}v{L}^{\prime },$$

(1)

Accordingly, the load-side voltage of the railgun is expressed as follows:

Here, $R^{\prime }x$ denotes the position-dependent rail resistance, $R_v\left(v\right)$ is an additional velocity-dependent dynamic resistance term, $L\left(x\right)$ is the equivalent rail inductance varying with the armature position x, $L^{\prime }=dL/dx$ is the rail inductance gradient, and v is the armature velocity. In Figure 5, the velocity-dependent and position-dependent parameter couplings are indicated explicitly, whereas the motion-induced term $i_{\mathrm{load}}v{L}^{\prime }$ is retained in Equation (1) as the compact system-level representation of the corresponding electromechanical coupling. In this form, the model does not explicitly resolve the electromagnetic-field redistribution associated with the velocity skin effect, nor does it explicitly track the detailed evolution of the armature–rail contact interface. Instead, these higher-order effects are implicitly accounted for through the equivalent resistance terms retained in the load model.

The electromagnetic thrust acting on the armature is given by:

$$F={\displaystyle \frac{1}{2}}{L}^{\prime }{i}_{\mathrm{load}}^2,$$

(2)

To reflect the main mechanical dissipation at system level, a simplified velocity-dependent friction term is included in the armature dynamics. The motion equation is therefore written as follows:

$$\begin{array}{cc}\hfill m{\displaystyle \frac{dv}{dt}}& ={\displaystyle \frac{1}{2}}{L}^{\prime }{i}_{\mathrm{load}}^2-F_{\mathrm{fr}}\left(v\right),\hfill \\ \hfill {\displaystyle \frac{dx}{dt}}& =v,\hfill \end{array}$$

(3)

Here, m is the armature mass and $F_{\mathrm{fr}}\left(v\right)$ is a smoothed velocity-dependent friction term. The resulting railgun load model is an electrically driven and position-coupled system in which the load current, armature motion, and dynamic load voltage evolve in a mutually dependent manner. This treatment preserves the dominant coupling among current build-up, armature acceleration, and load-voltage evolution while avoiding unnecessary numerical stiffness in the full XRAM topology model.

For reference, if the mechanical dissipation term is neglected, the armature speed can be approximated as follows:

$$v\left(t\right)={\displaystyle \frac{L^{\prime }}{2m}}{\int }_0^t{i}_{\mathrm{load}}^2\left(\tau \right)d\tau ,$$

(4)

This expression shows that the armature speed is not governed by the current peak at a single instant, but mainly by the time integral of the load-current square. Therefore, the maximum armature speed is taken as the primary performance index in this work, and the load-current-square integral is further employed as an auxiliary indicator of effective acceleration capability under different topologies and parameter combinations. In terms of scope, the adopted railgun model is intended for topology-level comparison, commutation-timing analysis, parameter optimization, and current–transfer mechanism evaluation. It is not intended as a detailed local model for contact-interface physics, full velocity-skin-effect resolution, or electrothermal stress prediction at the rail–armature interface.

2.3. ICCOS Module and Trigger Criterion

To enable controllable commutation in the XRAM topology, an ICCOS scheme is incorporated into each branch. Its function is twofold: interrupting the charging current at a well-defined instant and redirecting the stored inductor energy toward the railgun load. Figure 6 first summarizes the complete single-stage ICCOS commutation unit embedded in each branch, while Figure 7 isolates the three representative switching intervals used to explain the commutation sequence. The commutation unit for the kth branch comprises the precharged capacitor $C_k$, the charging thyristor $T{h}_k$, the branch diode $D_k$, three commutation diodes, $D_{k,1}$ through $D_{k,3}$, and the shared output switch $T{h}_G$. Figure 7a shows State I, in which the branch current is still carried by $T{h}_k$ while $C_k$ remains precharged and $T{h}_G$ is open. After $T{h}_G$ is triggered, as shown in Figure 7b, the capacitor discharges through the commutation loop and establishes a reverse current through the charging branch. As this reverse current grows to match the forward charging current, the net thyristor current drops below the holding threshold and $T{h}_k$ turns off naturally. Figure 7c then shows State III, where the stored inductor current is redirected to the load path and the residual capacitor voltage sustains the required reverse-bias interval across $T{h}_k$. What makes ICCOS particularly valuable here is not merely its ability to interrupt current, but its capacity to do so in a controlled, repeatable fashion that makes high-current thyristor operation in XRAM circuits practical.

Rather than treating the firing instant of the total output switch as a free control variable, a threshold-based triggering strategy is adopted in which the commutation is initiated when the residual voltage of the first-group main storage decays to a preset level. Let $v_{us1}\left(t\right)$ denote the residual voltage of the first-group main storage. The commutation-triggering instant $t_c$ satisfies:

$$v_{us1}(t_c;U_{S0})=U_{\mathrm{th}},$$

(5)

Here, $U_{S0}$ is the initial main-storage voltage and $U_{\mathrm{th}}$ is the ICCOS triggering threshold.

During the initial phase of energy release, current accumulates predominantly within the internal storage branches, and the load path remains effectively open. When the decaying main-storage voltage reaches $U_{\mathrm{th}}$, the ICCOS module fires, the commutation branch closes, and the system transitions into the current–transfer phase in which inductor energy begins flowing into the railgun load. From this point onward, the load current climbs steeply and armature acceleration becomes significant. The timing of this transition therefore shapes not only the commutation instant itself but also the width and magnitude of the main acceleration pulse and the overall speed output.

In this light, $U_{\mathrm{th}}$ operates as a timing knob for the entire energy-release rhythm. Setting it too low fires the ICCOS module prematurely, before the internal storage branches have accumulated sufficient current to sustain effective commutation. Setting it too high delays the transition, causing the load branch to miss the most energetically favorable window for current transfer. Selecting $U_{\mathrm{th}}$ correctly is therefore central to matching commutation timing to the energy-release dynamics, and it receives dedicated attention in the parameter optimization that follows.

The typical working process of the proposed topology is illustrated in Figure 8. The characteristic stages from energy build-up to main-pulse output provide the physical basis for the later analysis of output characteristics, parameter sensitivity, and current–transfer mechanism, and their state correspondence can be read together with the representative ICCOS configurations shown in Figure 7. Unless otherwise noted, the interval interpretation adopted in the subsequent waveform figures follows the same State I/II/III definitions introduced in Figure 7 and Figure 8.

2.4. Simulation Model and Comparison Principles

System-level simulation models of both topologies are constructed in Simulink. Each model includes the main-storage capacitors, reverse-commutation capacitors, multistage inductors, thyristors, diodes, and the coupled electromechanical railgun load. Device conduction and blocking, commutation establishment, and armature acceleration are captured in a unified framework, consistent with modeling approaches reported in [23,25].

The electronic-device representation adopted in this work is intentionally kept at the system level. Thyristors and diodes are modeled through their switching functionality and conduction/blocking states so that topology-level output timing, current transfer, and voltage stress can be compared on a consistent basis. Detailed electrothermal coupling, junction-capacitance dynamics, and fully distributed parasitic networks are therefore not explicitly resolved in the present study. Accordingly, the reported results should be interpreted as topology-level performance trends under lumped-parameter modeling assumptions rather than as a complete device-design study.

The baseline comparison is conducted on equal terms: the total number of stages, load parameters, major device ratings, and triggering strategy are held fixed across both topologies, while the total initial stored energy is kept equal and the working-voltage levels are kept comparable. To achieve this, the proposed topology draws on three independent main capacitors, whereas the conventional topology uses a single equivalent capacitor whose initial energy equals the combined energy of those three. The working voltage of this equivalent capacitor is set at the same order of magnitude as that of one group in the proposed topology so that neither design is artificially penalized or favored by an unrealistic voltage mismatch.

A second level of comparison, referred to throughout as the trigger-threshold-optimized comparison, is introduced specifically to test whether any observed performance gap is structural or merely a product of a suboptimal threshold setting. Here, the over-voltage constraint is lifted, the turn-off constraint is retained, and each topology independently sweeps $U_{\mathrm{th}}$ to locate its own best operating point under the same baseline electrical parameters. If the proposed topology still outperforms the conventional one under these conditions, the advantage must be attributed to an intrinsic difference in circuit behavior rather than to a favorable but arbitrary trigger choice.

2.5. Optimization Objectives and Constraints

The parameter optimization of the proposed three-module grouped XRAM pulsed power supply aims to maximize the output performance of the electromagnetic railgun while ensuring safe and feasible operation. Since the maximum armature speed directly reflects the energy-release capability of the pulsed power supply at the load, it is adopted as the primary optimization objective. In addition, the over-voltage and thyristor turn-off constraints are evaluated according to the device-stress and commutation considerations discussed in [17,18]. The optimization objective can be expressed as follows:

$$max{v}_{max}(U_S,U_{C,a},U_{C,b},U_{\mathrm{th}}),$$

(6)

The first constraint is the device over-voltage constraint. Let $V_{pk,max}$ denote the maximum peak voltage among all thyristors, and let $V_{allow}$ denote the allowed device peak voltage. Then:

$$V_{pk,max}\le V_{\mathrm{allow}},$$

(7)

In this work, $V_{\mathrm{allow}}$ is set to 3600 V, corresponding to an 80% usage margin of a 4.5 kV-class device.

The second constraint is the turn-off feasibility constraint. All thyristors involved in commutation must be normally turned off, and no turn-off failure is allowed, i.e.:

$$N_{\mathrm{turnoff}\mathrm{fail}}=0.$$

(8)

Here, $N_{\mathrm{turnoff}\mathrm{fail}}$ denotes the number of devices experiencing a turn-off failure. This constraint guarantees the physical realizability of the commutation process.

Consequently, the optimization problem studied in this paper is to identify the parameter combination that maximizes the armature speed subject to the over-voltage and turn-off-feasibility constraints. Therefore, the final recommended parameters are not merely mathematical extrema, but engineering compromise optima obtained within the safe operating boundary.

2.6. Evaluation Metrics

To quantitatively evaluate the output capability and the energy-transfer mechanism of the two topologies, several metrics are employed. The maximum armature speed $v_{max}$ is used to characterize the final output performance, and the peak voltage $V_{pk,max}$ is used to characterize the voltage stress of key devices. The remaining indices are introduced to explain how current–transfer timing and waveform shape contribute to the observed output differences.

In the mechanism analysis, the load-current-square integral is defined as follows:

$$J=\int i_{\mathrm{load}}^2\left(t\right)dt,$$

(9)

According to the railgun dynamics, J is directly related to the armature speed increase and can therefore be used as an effective index for comparing acceleration capability.

To avoid using only the current peak to describe the main pulse, the equivalent pulse width is defined as follows:

$$T_{eq}={\displaystyle \frac{J}{I_{\mathrm{peak}}^2}},$$

(10)

Here, $I_{peak}$ is the peak value of the load current. This metric represents the duration required for an equivalent rectangular pulse with the same peak current to produce the same acceleration contribution as the actual waveform.

To describe the overall transfer of the internal inductor current to the load branch, the total inductor current is defined as follows:

$$I_L\left(t\right)={\displaystyle \sum _{k=1}^{12}}{i}_{Lk}\left(t\right),$$

(11)

The instantaneous current–transfer ratio is defined as follows:

$$\beta \left(t\right)={\displaystyle \frac{i_{\mathrm{load}}\left(t\right)}{I_L\left(t\right)}},$$

(12)

Thus, $i_{\mathrm{load}}\left(t\right)=\beta \left(t\right)I_L\left(t\right)$, and the load-current-square integral can be rewritten as $\int {\beta }^2\left(t\right)I_L^2\left(t\right)dt$.

This expression indicates that the acceleration capability depends not only on the magnitude of the internal inductor current but also on the effective proportion transferred to the load.

To further characterize the overall transfer capability, the average current–transfer ratio is defined as follows:

$$\overline{\beta }={\displaystyle \frac{\int i_{\mathrm{load}}\left(t\right)I_L\left(t\right)dt}{\int I_L^2\left(t\right)dt}},$$

(13)

This definition is equivalent to a weighted average of $\beta \left(t\right)$ using $I_L^2\left(t\right)$ as the weighting function, thereby emphasizing the critical stages in which the total inductor current is large and contributes most to the acceleration process. It can also be interpreted as the least-squares equivalent coefficient when approximating $i_{\mathrm{load}}\left(t\right)$ by $I_L\left(t\right)$. Therefore, $\overline{\beta }$ is used to characterize the overall effectiveness with which the internal storage current is transferred to the load branch during commutation.

Based on the above topology description, load model, trigger criterion, constraints, and evaluation metrics, the subsequent sections first compare the two topologies under identical baseline parameters and then identify the parameter dependence and performance-advantage mechanism of the proposed topology.

3. Results

3.1. Output Characteristics Under Identical Baseline Parameters

With stage count, device ratings, load parameters, triggering strategy, total initial stored energy, and voltage level made comparable across both designs, the baseline comparison isolates the effect of topology structure on output behavior. The most immediate difference is temporal: the grouped topology opens a conducting path to the railgun load well before the conventional all-parallel arrangement does, indicating that the group-level partitioning accelerates the handover of stored energy to the load.

Figure 9 makes this timing difference concrete. The dashed markers identify the commutation-establishment instant for each design, and the grouped topology reaches this milestone appreciably earlier. The downstream effect is visible in the armature-speed trace: acceleration begins sooner and proceeds at a steeper rate, reflecting a more favorably timed output pulse rather than a simply larger one.

The voltage-stress picture in Figure 10 adds a second dimension to the comparison. In the conventional topology, the total output switch carries a disproportionately large and sustained blocking-voltage burden. The grouped architecture partially redistributes this initial duty to the leading device within each submodule group, as Figure 10a shows for representative branch thyristors and the output switch; Figure 10b then quantifies the peak magnitudes and their occurrence times. The advantage is therefore not a uniform reduction in device stress across the board, but a structural redistribution that spreads the burden more evenly while simultaneously advancing the moment at which the load comes online.

3.2. System-Level Loss Estimation and Parasitic-Parameter Considerations Under the Baseline Condition

To complement the voltage-stress and turn-off analysis, a system-level loss estimation was performed at the baseline operating points. The estimate includes the equivalent load-side resistive dissipation, thyristor conduction loss, and diode conduction loss, while detailed switching loss and temperature-dependent parameter drift are not explicitly modeled. In

Table 2. System-level loss estimation under the baseline condition.

Topology	${\mathit{E}}_{\mathbf{load},\mathbf{res}}$/J	${\mathit{E}}_{\mathbf{thy}}$/J	${\mathit{E}}_{\mathbf{dio}}$/J	${\mathit{E}}_{\mathbf{loss},\mathbf{tot}}$/J	${\mathit{E}}_{\mathbf{kin},\mathbf{end}}$/J
Conventional	11,814	57,882	7404	77,099	7977
Proposed	18,754	58,605	8884	86,242	12,109

, $E_{\mathrm{load},\mathrm{res}}$ denotes the cumulative resistive dissipation in the equivalent load-side resistance, $E_{\mathrm{thy}}$ denotes the cumulative thyristor conduction loss, $E_{\mathrm{dio}}$ denotes the cumulative diode conduction loss, $E_{\mathrm{loss},\mathrm{tot}}$ is the sum of the preceding dissipative terms, and $E_{\mathrm{kin},\mathrm{end}}$ is the final armature kinetic energy. The table therefore includes both internal conduction loss and load-side resistive dissipation, because both terms shape the system-level energy partition retained in the present model.

The grouped topology shows a larger total dissipative term in this system-level estimate, but it also delivers a substantially larger final armature kinetic energy. This behavior is physically consistent with the earlier load access and the stronger load-current response already identified in the waveform analysis: once more energy is transferred to the load branch at the appropriate time, both the useful output and the load-side resistive dissipation can increase simultaneously. For this reason, the system-level loss estimate should not be interpreted as contradicting the main conclusion of this paper; instead, it indicates that the grouped topology converts a larger portion of the stored energy into effective armature acceleration despite the stronger overall discharge process. The purpose of Table 2 is therefore not to provide a complete electrothermal evaluation, but to offer a compact comparison of the main dissipative channels retained in the present system-level model.

Parasitic effects were also assessed through a lumped-equivalent representation. In practice, the most relevant non-idealities of the ICCOS commutation loop are the lumped stray inductance and the equivalent series resistance of the commutation capacitor branch. Their influence can be approximated by an additional transient voltage contribution $\Delta V_{\sigma }\approx L_{\sigma }di/dt$ and an additional resistive drop $\Delta V_{\mathrm{ESR}}\approx i_C{R}_{\mathrm{ESR}}$, respectively. These terms primarily affect local transient stress and commutation margin by increasing voltage overshoot and weakening reverse-current support. Accordingly, they primarily modify absolute device-stress margins rather than the comparative ranking between the two topologies. In other words, practical parasitic parameters are expected to modify local safety margins, whereas the reported performance advantage of the grouped topology still originates primarily from earlier load access and more effective current transfer.

3.3. Parameter Optimization of the Proposed Topology

Parameter optimization of the proposed topology proceeds in three stages: single-factor sweeps to establish individual sensitivities, two-dimensional coupling maps to expose interaction effects and feasibility constraints, and a local four-dimensional refinement to identify the recommended operating point. The variables examined are $U_S$, $U_{C,a}$, $U_{C,b}$, and $U_{\mathrm{th}}$.

The single-factor results in Figure 11 draw a clear distinction between the roles of $U_S$ and $U_{\mathrm{th}}$. Increasing $U_S$ raises the overall energy level of the system and directly lifts the achievable speed ceiling; it is the dominant performance driver. $U_{\mathrm{th}}$, by contrast, leaves the stored energy unchanged and instead shifts the commutation instant, functioning as a fine-tuning lever for matching the output pulse to the acceleration window.

The two-dimensional parameter maps show that the feasible operating region is bounded by different physical constraints on different sides. In the $U_S$-$U_{\mathrm{th}}$ plane, Figure 12a reveals a well-defined speed ridge that confirms commutation timing is the critical variable along that axis. In the $U_S$-$U_{C,b}$ plane, Figure 12b shows that the high-parameter boundary is set by the device over-voltage limit—pushing $U_{C,b}$ too far eventually violates the voltage rating. At the opposite extreme, Figure 13a demonstrates that the low-parameter boundary is governed by turn-off feasibility: insufficient reverse-commutation support leads to thyristor turn-off failures that contract the usable domain from below.

Zooming into the high-performance region through the four-dimensional local refinement, Figure 13b shows that the optimum is not a sharp, numerically sensitive peak but a broad plateau over which performance remains high across a range of parameter combinations. Rechecking this region against the stable model yields the recommended parameter set listed in

Table 3. Recommended parameter set of the stable model after rechecking the local optimal region.

Parameter or Metric	Recommended Value
$U_S$	3520 V
$U_{C,a}$	2200 V
$U_{C,b}$	1840 V
$U_{\mathrm{th}}$	350 V
$v_{max}$	1905.84 m/s
$V_{pk,max}$	3599.33 V

, where the peak device voltage stays within the 80% usage margin. The existence of this plateau carries practical significance: the topology can be operated near its performance ceiling without requiring impractically tight parameter tolerances.

3.4. Scalability with Respect to Group Count

The grouped topology proposed in this paper is realized as a three-group, 12-module system, but the same design idea can be extended to other group counts. To clarify this point, the existing group-comparison results were further summarized under a constrained-comparison criterion that simultaneously accounts for usable commutation, output-switch stress, and reverse-voltage margin.

Table 4. Group-count scalability under the constrained-comparison criterion.

Group Count	Best Constrained ${\mathit{v}}_{\mathbf{max}}$ (m/s)	Best Constrained ${\mathit{t}}_{\mathit{c}}$ (ms)	Best Constrained ${\mathit{V}}_{\mathit{pk},\mathbf{max}}$ (V)	Constrained- Feasible Rate	Engineering Implication
1	1270.5	13.246	3961.8	0.000	No constrained-feasible point is retained; current transfer remains late and output-switch stress remains high.
2	1487.6	7.065	3452.1	0.989	A clear improvement appears once grouping is introduced, while a wide usable operating region is still preserved.
3	1565.8	4.762	2964.0	0.962	This case offers a balanced improvement in speed, commutation timing, voltage stress, and operating robustness.
4	1607.2	3.572	2527.3	0.921	Further performance improvement is obtained, although the feasible region begins to contract.
6	2310.6	2.168	1640.4	0.461	The speed ceiling continues to rise, but the feasible region shrinks markedly, indicating a more aggressive and less robust design space.

reports the best constrained operating point and the constrained-feasible rate for representative group counts. Here, the constrained-feasible rate denotes the proportion of scanned operating points that satisfy the combined engineering constraints used in the comparison.

The scalability trend is therefore not monotonic. Increasing the number of groups continuously improves commutation timing and suppresses the peak voltage stress at the best point, but the usable operating region does not remain equally broad as the partition becomes more aggressive. In particular, the six-group case delivers the highest speed ceiling, yet its constrained-feasible rate drops to 46.1%, which indicates a substantial contraction of the robust design space. Accordingly, the three-group arrangement is not presented as the unique mathematical optimum for every possible design objective. Instead, it is selected as a practical compromise for the 12-module system, because it already captures most of the structural benefit of grouping while retaining a broad feasible operating region and a comparatively moderate device-stress level.

4. Discussion

The previous section established the baseline advantages of the grouped topology and identified its preferred operating region under strict engineering constraints. Two questions still need to be answered. Does the same advantage remain when both topologies are allowed to optimize their own triggering thresholds? If it does, what physical process is responsible for the remaining performance gap?

4.1. Trigger-Threshold-Optimized Comparison of the Two Topologies

One possible explanation for the weaker performance of the conventional topology is simply that its default threshold setting is not favorable. To exclude this possibility, we carry out a trigger-threshold-optimized comparison. The over-voltage constraint is released, the thyristor turn-off condition is retained, and each topology independently sweeps $U_{\mathrm{th}}$ to locate its own best operating point. All other electrical parameters are kept the same.

The two topologies converge to their respective optima at quite different threshold levels. Even after this individual optimization, the grouped topology still reaches commutation earlier, operates with a lower peak device voltage, and achieves a substantially higher armature-speed ceiling, as shown in Figure 14 and summarized in

Table 5. Summary of the topology comparison results.

Comparison Level	Metric	Proposed Topology	Conventional Topology	Implication
Baseline comparison	$t_c$/ms	4.7577	13.3289	The grouped topology establishes commutation about 8.57 ms earlier.
Baseline comparison	$v_{max}$/(m/s)	1556.7	1263.5	The baseline armature-speed ceiling is about 23.2% higher for the proposed topology.
Baseline comparison	$V_{pk,max}$/V	2999.3	4042.4	The peak output-switch-related stress is about 25.8% lower in the proposed topology.
Trigger-threshold-optimized comparison	$U_{\mathrm{th}}$/V	365	880	The proposed topology reaches its optimum under a lower triggering threshold.
Trigger-threshold-optimized comparison	$t_c$/ms	4.7577	13.3290	The commutation establishment of the proposed topology is about 8.57 ms earlier.
Trigger-threshold-optimized comparison	$v_{max}$/(m/s)	1556.7	1264.6	The potential speed limit is about 23.1% higher for the proposed topology.
Trigger-threshold-optimized comparison	$V_{pk,max}$/V	2999.3	3999.2	The conventional topology reaches its optimum with a much higher voltage stress.
Trigger-threshold-optimized mechanism	$I_{peak}$/A	$2.3421\times {10}^5$	$2.5161\times {10}^5$	The conventional topology has a slightly higher current peak, but this is not the dominant factor.
Trigger-threshold-optimized mechanism	$J=\int i_{\mathrm{load}}^{2}dt$/${\mathrm{A}}^2·$s	$6.2653\times {10}^7$	$5.0918\times {10}^7$	The proposed topology provides a stronger effective acceleration action.
Trigger-threshold-optimized mechanism	$T_{eq}$/ms	1.1421	0.8043	The proposed topology maintains a longer equivalent high-current action time.
Trigger-threshold-optimized mechanism	$\overline{\beta }$	0.3777	0.1928	The proposed topology transfers the internal storage current to the load more effectively.

. The performance margin therefore cannot be attributed to a poorly chosen trigger setting; it persists after the comparison is placed on equal footing.

4.2. Mechanism Interpretation Based on Current Integral and Transfer Ratio

Figure 15a shows an important detail of the load-current response. The conventional topology does reach a slightly higher peak current, but the pulse is narrow and arrives relatively late in the acceleration process. The grouped topology behaves differently: it builds current earlier and sustains a stronger load-driving level over the more useful portion of the acceleration window. This distinction is captured more faithfully by the load-current-square integral $J=\int i_{\mathrm{load}}^2\left(t\right)dt$ and the equivalent pulse width $T_{eq}$, shown in Figure 15b.

The data in Table 5 confirm the same point. At the respective optimized operating points, the grouped topology has a slightly lower peak current, yet both J and $T_{eq}$ are larger. The higher armature speed therefore does not come from a sharper current spike. It comes from maintaining an effective driving current for a longer interval.

The current–transfer process offers the deeper explanation. Figure 16 shows that the conventional topology can retain a larger total inductor current during much of the discharge, but a larger portion of that current remains trapped in the internal storage branches. By contrast, the grouped topology exhibits an earlier and steeper rise in the transfer ratio $\beta \left(t\right)=i_{\mathrm{load}}\left(t\right)/I_L\left(t\right)$, where $I_L\left(t\right)$ is the total inductor current. Its mean transfer ratio $\overline{\beta }$ is also substantially higher, as listed in Table 5. In other words, the grouped architecture is not simply storing current well; it is delivering a larger fraction of that current to the load at the right time.

These observations point to two coupled reasons for the performance advantage of the grouped topology. It establishes commutation earlier, and it transfers internal storage current to the load more effectively. Together, these effects raise J, extend $T_{eq}$, and ultimately produce a higher armature-speed ceiling.

5. Conclusions

This study examined a three-module grouped XRAM topology for electromagnetic railgun drive, with emphasis on its output behavior, parameter sensitivity, and commutation mechanism.

When the two topologies are compared under equal initial stored energy and comparable voltage levels, the grouped topology connects to the railgun load earlier than the conventional all-parallel topology. This earlier load access leads to a faster rise in armature speed and reduces the blocking-voltage burden on the total output switch by redistributing part of the initial stress to the leading devices of each group.

The parameter study also clarifies the roles of the key design variables. The main-storage voltage $U_S$ determines the overall energy level and the achievable speed ceiling, whereas the triggering threshold $U_{\mathrm{th}}$ mainly adjusts the commutation timing. The reverse-capacitor voltages define the feasible operating boundaries associated with over-voltage and turn-off constraints.

The trigger-threshold-optimized comparison further shows that the advantage of the grouped topology is structural. Even when each topology is allowed to optimize its own threshold, the grouped design still delivers a higher armature speed despite a slightly lower peak current. The reason is that it establishes commutation earlier and channels internal storage current into the railgun load more effectively.

Overall, the grouped XRAM topology provides a more effective way to deliver stored energy to the railgun load than the conventional parallel arrangement. Future work will focus on experimental validation, the inclusion of additional device non-idealities, and adaptation of the topology to different energy levels.