# Inversion-based Control Simplifications for a Cycling-mode Power Converter in Particle Accelerators

Amel Baziz, Dimitris Xystras, Gilles Le Godec, Philippe Delarue, Alain Bouscayrol

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Amel Baziz, Dimitris Xystras, Gilles Le Godec, Philippe Delarue, Alain Bouscayrol. Inversion-based Control Simplifications for a Cycling-mode Power Converter in Particle Accelerators. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0280. hal-05082310

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# Inversion-based Control Simplifications for a Cycling-mode Power Converter
in Particle Accelerators

Amel Baziz¹, Dimitris Xystras², Gilles Le Godec², Philippe Delarue¹, Alain Bouscayrol¹.

¹UNIV. LILLE, ARTS ET METIERS INSTITUTE OF TECHNOLOGY, CENTRALE
LILLE, JUNIA, ULR 2697 - L2EP
F-59000 Lille, France.

E-mail : alain.bouscayrol@univ-lille.fr

² EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

Esplanade des Particules 1, 1211 Geneva, Switzerland.

## Keywords

«Energy storage», «Converter control», «Particle accelerator», «Energetic Macroscopic Representation».

## Abstract

This paper analyzes control simplifications for a high-accuracy power converter with energy recovery capability used to supply electromagnets in particle accelerators. The Energetic Macroscopic Representation (EMR) graphical formalism is used to organize the system model and its control, which are validated through simulation and experimental results. The results indicate that achieving high accuracy for the magnet current using cascaded PI controllers necessitates a full control structure with the maximum number of measurements and control actions, at cost of additional sensors and complex implementation. Although control structure simplifications compromise accuracy specifications, the controllability remains ensured.

## Introduction

A particle accelerator requires the use of electromagnets (magnets) to control the trajectory of particle beams. The high power demand during the injection, acceleration, and guiding of particles requires the use of modular power converters connected in series and/or in parallel. The main objective is an accurate control of the magnet current. However, energy recovery is also of interest to reduce energy consumption and consequently, lower power demand from the grid. To achieve this, energy storage units are added to an initial power converter topology to recover the reactive energy of the magnet or a part of it.

POLARIS [1] is a new topology of a modular power converter with energy recovery capability. This topology is going to be employed in replacing obsolete converters during a consolidation program at CERN [2]. Operating in power cycling mode, POLARIS power converters feature recovery of the magnets stored energy into built-in electrolytic capacitors storage. This energy recovery is implemented based on energy management strategies [3]-[4]-[5]. POLARIS control structure is implemented using PI controllers and follows cascaded voltage and current loops structure.

EMR (Energetic Macroscopic Representation) is a graphical formalism for control complex energy conversion systems [6]. The system is decomposed into elementary subsystems. These elements are inverted by dedicated control operations including explicit disturbance compensations. If this method leads to an important number of measurements and control operations, it enables achieving high accuracy by using cascaded loops. Notable work has been carried out in the domain of power converters control in particle accelerators using EMR and inversion-based methodology [7]-[8]-[9]-[10].

The present study analyzes the inversion-based control simplifications for POLARIS power converter and their impact on the loops stability and the output current accuracy.

The second section deals with the study of an initial system without energy storage for the validation of the EMR-based control model. The third section focuses on the inversion-based control of POLARIS power converter (including energy storage subsystem). The last section addresses the simplifications in the inversion-based control structure and their impact on the required accuracy.
# Initial System without Energy Recovery

## Topology of the initial system

The topology of (Fig. 1) illustrates a power converter for particle accelerators with a simplified input stage. The topology is composed of a controlled voltage source connected on the DC-link, an H-bridge operating as a DC-DC converter and an output high frequency filter. The purpose is to organize the control scheme of the output stage of the power converter based on EMR principles.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Topology of the initial system without storage.</figcaption></figure>

## EMR and control of the initial system

EMR is a graphical formalism for system and model organization. As the system is decomposed into basic subsystems in interactions, it translates the set of their mathematical equations into different graphical pictograms. The graphical elements are (see Appendix A): energy source (green oval), accumulation element with energy storage (crossed orange rectangle), conversion element without energy storage (orange square), coupling elements without energy storage (overlapped orange squares). These elements are linked by arrows symbolizing the interaction variables between the various subsystems [11]. All the components involved are described using mathematical expressions. As all the variables are assumed measurable by hypothesis.

In this study, the DC-link modeled as a controlled voltage source that delivers $u_{dc}(t)$ is described by an energy source (green oval) according to EMR.

The H-bridge converter is modeled in average values [12] to modulate the voltage $u_f(t)$ and the current $i_{ch}(t)$ using the modulation function $m_1(t)$. In EMR, it is described by a conversion element (orange square).

$$ 
\begin{aligned}
u_f(t) &= m_1(t)u_{dc}(t) \\
i_{ch}(t) &= m_1(t)i_f(t)
\end{aligned}
\quad (1) $$

The filter inductor is modelled by an equivalent $L-R$ circuit with the current $i_f(t)$ as a state variable that derives from the voltages $u_f(t)$ and $u_m(t)$, where $L_f$ is

the inductance and $R_f$ is the internal resistance and. In EMR, it is described by an accumulation element (crossed orange rectangle).

$$ L_f \frac{di_f(t)}{dt} + R_f i_f(t) = u_f(t) - u_m(t) \quad (2) $$

The filter capacitor is modeled by an ideal capacitance with the voltage $u_m(t)$ as a state variable that derives from the currents $i_f(t)$ and $i_m(t)$. Another accumulation element is used.

$$ C_f \frac{du_m(t)}{dt} = i_f(t) - i_m(t) \quad (3) $$

The magnet is modeled by an equivalent $L-R$ circuit with the current $i_m(t)$ as a state variable that derives from the voltage $u_m(t)$, where $L_m$ is the inductance and $R_m$ is the internal resistance. In EMR, it is described by another accumulation element (crossed orange rectangle).

$$ L_m \frac{di_m(t)}{dt} + R_m i_m(t) = u_m(t) \quad (4) $$

The model is thus organized using EMR (Fig. 2). All the elements are connected according to the action and reaction principle using exchange variables (arrows).

<figure><img src="image_3.png" /><figcaption>Fig. 2: EMR of the initial system model.</figcaption></figure>

To control the magnet current, a tuning path is defined from $m_1(t)$ to $i_m(t)$ (Fig. 3). The inversion of the tuning path allows the obtention of the control path to impose $i_{m,ref}(t)$.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Tuning path of the initial system.</figcaption></figure>

The control scheme of the system is obtained using the inversion principle [11]-[13]. The inversion of the magnet inductor $L_m$ is obtained by the indirect inversion of (4). It is achieved using a PI controller $C_{im}(t)$ with $i_{m,meas}(t)$ the measurement of the magnet current. This leads to the reference voltage $u_{m,ref}(t)$ (5). In EMR, it is described by an indirect inversion element (crossed blue parallelogram).
$$u_{m,ref}(t) = C_{i_m}(t)[i_{m,ref}(t) - i_{m,meas}(t)] \quad (5)$$

The inversion of the filter capacitor $C_f$ is obtained by the indirect inversion of (3). It is achieved using a PI controller $C_{u_m}(t)$ with $u_{m,meas}(t)$ the measurement of the filter capacitor voltage. The magnet current $i_{m,meas}(t)$ is a disturbance highlighted by EMR. It is added as a compensation by a feedforward action. This leads to the reference voltage $i_{f,ref}(t)$ (6). Note that the added compensation (dashed line) is not mandatory. In EMR, this control law is described by an indirect inversion element (crossed blue parallelogram).

$$i_{f,ref}(t) = C_{u_m}[u_{m,ref} - u_{m,meas}] + i_{m,meas} \quad (6)$$

The inversion of the filter inductor $L_f$ is obtained by the indirect inversion of (2). It is achieved by using a PI controller $C_{i_f}(t)$ with $i_{f,meas}(t)$ the measurement of the filter inductor current. The magnet voltage $u_{m,meas}(t)$ is added as a compensation by feedforward. This leads to the reference voltage $u_{f,ref}(t)$. In EMR, it is described by an indirect inversion element (crossed blue parallelogram).

$$u_{f,ref}(t) = C_{i_f}[i_{f,ref} - i_{f,meas}] + u_{m,meas} \quad (7)$$

The inversion of the DC-DC converter is obtained from a direct inversion of (1). This leads to reference modulation function $m_{1,ref}(t)$, with $u_{dc,meas}(t)$ the measurement of the DC-link voltage. In EMR, it is described by a direct inversion element (non-crossed blue parallelogram).

$$m_{1,ref}(t) = \frac{u_{f,ref}(t)}{u_{dc,meas}(t)} \quad (8)$$

All the controllers and inversions are connected to obtain the Maximal Control Structure (MCS), consisting of cascaded control voltage and current loops with all feedforward compensations (Fig. 4). In fact, this structure includes a maximal number of control loops and measurements [11].

<figure><img src="image_5.png" /><figcaption>Fig. 4: Inversion-based control of the magnet current.</figcaption></figure>

## Experimental validation of the initial system

To validate the inversion-based control of magnet current, simulation results are compared to experimental ones. Tests are conducted on SIRIUS [14], a power converter developed at CERN. The topology of SIRIUS (Fig. 5) is identical to the topology of Fig. 1 with the controlled voltage source implemented by a transformer, a rectifier and a boost converter. SIRIUS is able to operate in cycling mode with maximum output ratings of 450 V and 450 A [14].

<figure><img src="image_6.png" /><figcaption>Fig. 5: SIRIUS power converter for experimental results of the initial system.</figcaption></figure>

Table I presents the parameters of the magnet and power converter. Specifically, the Slew Rate SR is the slope of the magnet current during ramp-up and ramp-down phases.

<table><caption>Table I: Experimental parameters values</caption><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>Initial DC-link voltage</td><td>U<sub>dc,init</sub> = 900 V</td></tr><tr><td>Magnet inductance</td><td>L<sub>m</sub> = 67.35 mH</td></tr><tr><td>Magnet resistance</td><td>R<sub>m</sub> = 61.35 mΩ</td></tr><tr><td>Maximal magnet current</td><td>I<sub>m,max</sub> = 300 A</td></tr><tr><td>Slew Rate</td><td>|SR| = 292 A/s</td></tr><tr><td>Cycle duration</td><td>t<sub>cycle</sub> = 14.4 s</td></tr></tbody></table>

Experimental results for the initial system include DC-link voltage $u_{dc}(t)$, magnet voltage $u_m(t)$, and magnet current $i_m(t)$, as obtained from SIRIUS converter (Fig. 6). The magnet current waveform is trapezoidal for power cycling mode operations.
<figure><img src="image_7.png" /><figcaption>Fig. 6: Experimental DC-link voltage, magnet voltage and current obtained on a real converter.</figcaption></figure>

In the simulation, the input stage of the SIRIUS converter is modeled as a controlled voltage source in MATLAB-Simulink ©. The controlled voltage source delivers the DC-link voltage $u_{dc}(t)$, which is experimentally measured and reproduced in the simulation. Note that this voltage is obtained through a specific strategy that is not detailed in this paper.

The sampling frequency $f_{sm}$ is equal to the apparent frequency at the output of the H-bridge $f_{sm} = 2 \cdot f_{sw} = 12$ kHz, where $f_{sw} = 6$ kHz is the switching frequency of the DC-DC converter. Two cycles are simulated to obtain the magnet current and voltage for the inversion-based control for the initial system (Fig. 7).

<figure><img src="image_8.png" /><figcaption>Fig. 7: DC-link voltage, magnet current and voltage obtained by simulation.</figcaption></figure>

Compared to the experimental results obtained from the initial power converter (SIRIUS), the simulation results

show concordance. Based on this, the simulation tool organized using EMR and the deduced inversion-based control are validated.

# System with Local Energy Recovery

## Topology of Polaris Power Converter

Compared to the initial system, the new system of POLARIS power converter includes a capacitor bank for energy storage (Fig. 8). An intermediate stage for energy recovery is added in parallel to the DC-link. It consists of a storage unit and a smoothing inductor added through a two-quadrant (2Q) converter to control power flow [3]. Decoupling the storage unit from the DC-link through the 2Q converter allows theoretically its full discharge, increasing its usability.

The energy unit is a local recovery system used to store the reactive energy of the magnet or a part of it. One energy storage is composed of 10 electrolytic capacitors (25 mF/400 V) making it a total capacitance of $C_{st,unit} = 0.25$ F. One single brick of POLARIS converter can host up to 3 storage units. The storage unit is operated at $U_{st,max} = 330$ V and allows a voltage swing of 200 V. The role of POLARIS power converter is to supply energy to the magnet while balancing energy transfer between the electrical grid and the storage unit. This effectively reduces the power demand from the grid [4].

Its simplest configuration consists in one single brick with cycling ratings of 360 V and 400 A for voltage and current respectively. A constant power of 50 kW can be delivered, while the peak power supplied to the magnet is 150 kW [1].

<figure><img src="image_9.png" /><figcaption>Fig. 8: POLARIS power converter with energy storage.</figcaption></figure>
## EMR and control of the system with energy storage

The modeling and representation of the initial system using EMR (Fig. 2) remain unchanged. However, since the 2Q converter is added in parallel to the H-bridge (9), it is described in EMR by a coupling element (overlapped orange squares). With $i_{dc}(t)$ and $i_{2q}(t)$, respectively the currents from the input stage and the 2Q converter.

$$i_{ch}(t) + i_{2q}(t) = i_{dc}(t) \quad (9)$$

The 2Q converter is modeled in average values which modulates the voltage $u_{2q}(t)$ and the current $i_{2q}(t)$ using the modulation function $m_2(t)$. In EMR, it is described by a conversion element (orange square).

$$\begin{cases} u_{2q}(t) = m_2(t)u_{dc}(t) \\ i_{2q}(t) = m_2(t)i_{st}(t) \end{cases} \quad (10)$$

The smoothing inductor is modeled by an equivalent $L-R$ circuit with the current $i_{st}(t)$ as a state variable that derives from the voltages $u_{2q}(t)$ and $u_{st}(t)$, where $L_{st}$ is the inductance and $R_{st}$ is the internal resistance. In EMR, it is described by an accumulation element (crossed orange rectangle).

$$L_{st} \frac{di_{st}(t)}{dt} + R_{st}i_{st}(t) = u_{2q}(t) - u_{st}(t) \quad (11)$$

The storage unit is modeled by a capacitance with the voltage $u_{st}(t)$ as a state variable that derives from the current $i_{st}(t)$. In EMR, it is described by an accumulation element (crossed orange rectangle).

$$C_{st} \frac{du_{st}(t)}{dt} = i_{st}(t) \quad (12)$$

The POLARIS power converter model is obtained by connecting and adding all the elements to the EMR of the initial system model (Fig. 9).

<figure><img src="image_10.png" /><figcaption>Fig. 9: EMR of the POLARIS power converter model.</figcaption></figure>

The recovery of the magnet reactive energy is achieved by directly controlling the voltage of the storage unit $u_{st}(t)$. In this process, a tuning path is defined from $m_2(t)$ to $u_{st}(t)$ (Fig. 10). The inversion of the tuning path allows obtaining the control path to impose $u_{st,ref}(t)$.

<figure><img src="image_11.png" /><figcaption>Fig. 10: Tunning path for the control of storage unit voltage.</figcaption></figure>

The voltage reference $u_{st,ref}(t)$ (13) is obtained using Energy Balance (EB) strategy [4]. The strategy is based on exchanging magnet reactive energy with the storage unit. Based on the principle of power conservation, the grid supplies only the energy required to compensate for magnet losses.

$$u_{st,ref}(t) = \sqrt{U_{st,max} - \frac{L_{st}}{C_{st}}i_{m}(t)^2} \quad (13)$$

The inversion of the storage capacitor $C_{st}$ is obtained by the indirect inversion of (12). It is achieved using a PI controller $C_{u_{st}}(t)$ with $u_{st,meas}(t)$ the measurement of the storage unit voltage. This leads to the reference current $i_{st,ref}(t)$ (14). In EMR, it is described by an indirect inversion element (crossed blue parallelogram).

$$i_{st,ref}(t) = C_{u_{st}}[u_{st,ref} - u_{st,meas}] \quad (14)$$

The inversion of the smoothing inductor $L_{st}$ is achieved through the indirect inversion of (11). It is achieved using a PI controller $C_{i_{st}}(t)$ with $i_{st,meas}(t)$ the measurement of the storage unit current. The storage unit voltage $u_{st,meas}(t)$ is a compensation added by feedforward. This leads to the reference voltage $u_{2q,ref}(t)$ (15). In EMR, it is described by an indirect inversion element (crossed blue parallelogram).

$$u_{2q,ref}(t) = C_{i_{st}}[i_{st,ref} - i_{st,meas}] + u_{st,meas} \quad (15)$$

The inversion of the 2Q converter is obtained from a direct inversion of (10). It leads to the reference modulation function $m_{2,ref}(t)$ (16), with $u_{dc,meas}(t)$ the DC-link voltage. In EMR, it is described by a direct inversion element (non-crossed blue parallelogram).

$$m_{2,ref}(t) = \frac{u_{2q,ref}(t)}{u_{dc,meas}(t)} \quad (16)$$
<figure><img src="image_12.png" /><figcaption>Fig. 11: EMR-based control of POLARIS power converter.</figcaption></figure>

Similarly, all the controllers and inversions are connected to obtain the Maximal Control Structure (MCS), for storage unit voltage control (Fig. 11) [15].

## Benefit of the system with energy storage

The POLARIS power converter model and its control are implemented in MATLAB-Simulink ©. The simulation uses the magnet, storage and power cycle parameters from Table II. The storage unit is designed to fully recover the magnet reactive energy $E_m$ using Energy Balane (EB) strategy [4]. Therefore, three units are required, with a total capacitance of $C_{st,brick}$.

<table><caption>Table II: Experimental parameters values</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Magnet inductance</td><td>L<sub>m</sub> = 0.711 H</td></tr><tr><td>Magnet resistance</td><td>R<sub>m</sub> = 0.508 Ω</td></tr><tr><td>Maximal Magnet current</td><td>I<sub>m,max</sub> = 270 A</td></tr><tr><td>Slew Rate</td><td>|SR| = 382.86 A/s</td></tr><tr><td>Magnet energy</td><td>E<sub>m</sub> = 25.916 kJ</td></tr><tr><td>Initial Storage unit voltage</td><td>U<sub>st,max</sub> = 330 V</td></tr><tr><td>Maximal Storage unit capacitance</td><td>C<sub>st,brick</sub> = 0.75 F</td></tr><tr><td>Maximal Storage unit energy</td><td>E<sub>st,brick</sub> = 34.5 kJ</td></tr><tr><td>Flat-top duration</td><td>t<sub>top</sub> = 4.8 s</td></tr><tr><td>Cycle duration</td><td>t<sub>cycle</sub> = 14.4 s</td></tr></tbody></table>

Two cycles are simulated to obtain the magnet current and voltage of the EMR-based control for POLARIS power converter (Fig. 12).

The stored energy is supplied during ramp-up and recovered during ramp-down for the next cycle following the current $i_{st}(t)$. During flat-top $t_{top}$, the storage unit

voltage $u_{st}(t)$ remains constant, as no energy exchange occurs (Fig. 13).

<figure><img src="image_13.png" /><figcaption>Fig. 12: Magnet current and voltage of the EMR-based control of POLARIS.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 13: Storage unit current and voltage using EB strategy.</figcaption></figure>
In accordance with the principle of power conservation, the grid only compensates for the losses $P_{g,avrg}(t)$ in average values. This leads to an important reduction in power consumption compared to the initial system (Fig. 14). The key benefit is that the storage unit manages the magnet power peaks $P_{st,avrg}(t)$, resulting in a significant reduction of peak power demand from the grid, thus achieving peak shaving. This is beneficial for the design of the AC infrastructure upstream of the power converter, lowering the installation costs.

<figure><img src="image_15.png" /><figcaption>Fig. 14: Grid and storage average power using EB strategy.</figcaption></figure>

# Control Simplification of the System with Energy Storage

## Simplification of the energy storage voltage control

The MCS is a theoretical control structure composed of a maximum number of operations and measurements on the system. Practical Control Structures (PCS) can be deduced through simplifications [15]. These structures are based on compromises or choices related to the system technical requirements and the controllers performances. These simplifications may reduce control performance in favor of lower cost or easier implementation.

The system organized using EMR highlights the simplifications that can be considered on the energy storage voltage structure (dashed lines). The compensation for the storage unit voltage $u_{st,meas}(t)$ is

simplified in the inversion of the smoothing inductor $L_{st}$ (Fig. 15).

<figure><img src="image_16.png" /><figcaption>Fig. 15: Storage unit current without the compensation of $u_{st}(t)$.</figcaption></figure>

First, the results show that despite the control structure simplifications, the stability of the control loops are not affected. Additionally, the storage unit current $i_{st}(t)$ remains within its limits, maintaining $-400 \text{ A} < i_{st}(t) < 400 \text{ A}$. The peak shaving is achieved for the power drawn from the grid, ensuring full recovery of the magnet reactive energy. Moreover, the use of a PI controller with relatively fast dynamics allows perturbations rejection. This simplifies the control implementation.

## Simplification of the magnet current control

In this case, two simplifications can be considered:

1. The compensation of the magnet current $i_m(t)$ for the inversion of the filter capacitor $C_f$.

2. The compensation of the magnet voltage $u_m(t)$ for the inversion of the filter inductor $L_f$.

For both the inversion of (1) and (10), the measurement of the DC-link voltage $u_{dc,meas}(t)$ has been replaced by its average value $U_{dc,avrg}$. This reduces the number of required sensors. Simulation results show that the use of the Maximal Control Structure (MCS) allows achieving the high accuracy requirement for the magnet current during flat-top. However, the compensations are simplified to derive a practical control structure (Fig. 16) with the controllers performing the regulation function to reject the perturbations. While this approach simplifies control implementation, it does not meet the accuracy requirements during flat-top as the error exceeds 10 ppm (Fig. 17). However, the stability of the control loops is still ensured.
<figure><img src="image_17.png" /><figcaption>Fig. 16: EMR for POLARIS power converter with control simplifications.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 17: Error of the magnet current during flat top.</figcaption></figure>

## Analysis of control simplifications

Previous results allow the implementation of various simplified control structures for the storage unit voltage regulation. These structures preserve the stability of control loops as the implementation complexity is reduced. Additionally, the recovery of the magnet reactive energy is not affected, as all the variables remain within the limits outlined in the technical specifications. However, achieving high accuracy for the magnet current necessitates maintaining the full control structure without simplifications. The implementation of the Maximal Control Structure (MCS), although demanding in terms of measurements and control operations, meets the high accuracy requirements. In this study, all compensations are added by feedforward as PI controllers track the references. Based on this approach, the overall EMR-based control is implemented for magnet current tracking and storage voltage regulation.

## Conclusion

Control structure simplifications are studied for the POLARIS power converter with energy recovery capability using Energetic Macroscopic Representation (EMR).

First, the system model without energy storage is organized using the EMR approach. The Maximal Control Structure (MCS) is implemented for magnet current tracking, based on the inversion-based control method. Experimental results validate this approach, demonstrating that EMR efficiently organizes complex systems and their control.

Next, the POLARIS power converter model with an integrated storage unit is organized using EMR. An EMR-based control is developed for storage unit voltage regulation. By using Energy Balance (EB) strategy, an appropriate energy management —developed at CERN—the reactive energy from the magnet is fully recovered and reused in the next cycle, reducing the power demand from the grid. Simulation results concluded that achieving high output accuracy, the MCS, which consist, in this case, of cascaded PI control loops with all feedforward compensations, is required, at the cost of additional sensors. However, for systems with lower accuracy requirements, certain control simplifications can be applied, maintaining controllability while reducing implementation complexity [15].

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<table><caption>Appendix: EMR pictograms</caption><tr><td>Source element (energy source)</td><td>Accumulation element (energy storage)</td><td>Indirect inversion (closed-loop control)</td></tr><tr><td>Mono-physical conversion element</td><td>Mono-physical coupling element (energy distribution)</td><td>Direct inversion (open-loop control)</td></tr><tr><td>Multi-physical conversion element</td><td>Multi-physical coupling element (energy distribution)</td><td>Coupling inversion (energy criteria)</td></tr></table>