Hello! Welcome to the next lesson in our course on high-field magnet systems.
In the previous lesson, we explored how the immense kinetic energy of a massive, rotating flywheel could be converted into long electrical pulses to power magnets. This technique of inertial energy storage, using motor-generators and homopolar generators, is a powerful solution for creating pulses lasting hundreds of milliseconds to seconds.
Today, we will investigate another advanced method for powering pulsed magnets, one that stores energy not mechanically, but electromagnetically. This brings us to the topic of Superconducting Magnetic Energy Storage (SMES). This technology leverages the unique properties of superconductors to create a highly efficient, rechargeable "battery" for magnetic field pulses and is being actively explored by major high-field laboratories.
This lesson addresses the learning outcome: Describe the principles of Superconducting Magnetic Energy Storage (SMES) for high-efficiency pulsed power. We will examine how a SMES system works, how it interfaces with a pulsed magnet, and the key design principles and challenges involved.
1. The Fundamental Principle of SMES
At its core, a Superconducting Magnetic Energy Storage (SMES) system is a large inductor made from a superconducting wire. The principle is elegantly simple and relies on the defining property of a superconductor: zero electrical resistance in the DC state.
When a current is established in a superconducting coil of inductance , a magnetic field is generated, and energy is stored within this field. The amount of stored energy is given by the familiar equation:
Because the coil has no resistance, once it is charged and short-circuited, the current will flow indefinitely (in what is called a "persistent mode"), and the magnetic energy is stored with almost no loss. To release the energy, the short-circuit is opened, and the coil is connected to a load.
To understand the basic concept and its advantages, please read the following short introduction.
Superconducting magnetic energy storage and ...
This excerpt from the paper 'Superconducting magnetic energy storage and related protection challenges' by Ciceron et al. provides a concise explanation of the SMES principle and compares its energy density to other technologies.
Please read Section 1.1, 'SMES principle'. Pay attention to the definition of stored energy and the comparison of volumetric energy density between a SMES system and high-power capacitor banks.
As the paper highlights, the energy density of SMES can be an order of magnitude higher than that of capacitors. This, combined with very high charge/discharge efficiency (often >95%) and a virtually unlimited cycle life, makes SMES an attractive technology for high-power applications.
The main components of a SMES system are shown in the diagram below.
2. Energy Transfer: From SMES to Pulsed Magnet
While storing energy is one part of the challenge, the other is transferring that energy efficiently to the pulsed magnet coil and, crucially, recovering it. This is where the Power Conditioning System (PCS) comes in. The PCS is a sophisticated set of power electronics (inverters, converters) that acts as a gatekeeper, precisely controlling the energy flow.
A recent study from the National High Magnetic Field Laboratory (NHMFL) explored using a SMES to power a section of their 100 T multi-shot magnet, which is currently powered by a massive motor-generator. This provides an excellent, practical case study.
Superconducting Magnetic Energy Storage for Pulsed ...
This paper, 'Superconducting Magnetic Energy Storage for Pulsed Power Magnet Applications,' details a simulation of using a SMES to drive a real-world pulsed magnet. It clearly explains the circuit topology and the energy transfer process.
Please read the Abstract and Introduction (Section I) to understand the context, then focus on Section II, 'ENERGY REQUIREMENT CALCULATION'. Pay close attention to: The simplified electrical circuit in Figure 2, which shows the SMES coil and the magnet load connected via two H-bridges and a linking capacitor. The description of how the system operates: one H-bridge controls the voltage from the SMES, while the other controls the current delivered to the magnet. The concept of bi-directional energy flow. Note the current profiles in Figures 4 and 6, showing the current dropping in the SMES as it rises in the magnet, and vice-versa.
The key takeaway from this study is the high efficiency of energy recovery. The simulation showed that after delivering a 3.5 MJ pulse to the magnet, about 2 MJ were recouped by the SMES coil at the end of the pulse. Only 1.5 MJ were dissipated. This is a stark contrast to a simple capacitor-discharge system where nearly all the energy is eventually dissipated as heat.
This high efficiency is a game-changer for repetitively pulsed magnets, as it dramatically reduces the average power drawn from the grid and lessens the cooling requirements between pulses.
Test your understanding!
In the NHMFL study (resource LINK), the SMES coil started with 45 MJ of stored energy and its current dropped from 30 kA to 25.5 kA during the pulse. After the pulse, the current recovered to 29.1 kA. Why doesn't the current return to the full 30 kA? Where did the "missing" energy go?
Show answer
The energy corresponding to the drop from 30 kA to 29.1 kA was lost from the system. This loss is primarily due to Joule heating in the resistive components of the circuit. While the SMES coil and the magnet coil itself (if superconducting) have no resistance, the magnet coil in a pulsed system is typically made of a normal conductor (like copper alloy). During the pulse, energy is dissipated as heat () in the magnet windings. There are also smaller losses in the power electronics. The SMES must be "topped off" from the grid between pulses to compensate for this lost energy.
3. Design Principles of a SMES Coil
Designing a SMES coil for a pulsed power application involves a complex multi-physics optimization problem, balancing electromagnetics, solid mechanics, and material science. Your background in these areas is directly applicable here.
3.1. Geometry and Inductance Optimization
For a given amount of superconducting wire, the goal is often to maximize the inductance to store the most energy for a given current. For a simple solenoid, the geometry can be defined by its inner radius and two dimensionless parameters: (aspect ratio of radii) and (aspect ratio of length to radius).
Superconducting Magnetic Energy Storage for Pulsed ...
The NHMFL paper also provides an excellent overview of the design process for the SMES solenoid itself.
Please read Section III.A 'Design Parameters' and III.B 'Minimum Volume Calculation'. Note the definitions of \alpha and eta and the formula for inductance (Equation 4). The key result is the concept of the Brooks coil (\alpha \approx 2, eta \approx 0.5), which is the geometry that yields the maximum inductance for a fixed length of conductor (or, equivalently, the minimum winding volume for a fixed inductance).
The Brooks coil is a fundamental starting point in solenoid design, though other constraints often require deviations from this ideal shape.
3.2. Mechanical Stress and the Virial Theorem
A SMES coil storing megajoules of energy is subjected to immense internal Lorentz forces that try to tear it apart. As you'll recall from our early lessons on the Maxwell stress tensor, these forces lead to significant mechanical stress.
A profound insight into this problem comes from the Virial Theorem as applied to magnetic fields.
Superconducting magnetic energy storage and ...
Let's return to the paper by Ciceron et al. to understand the fundamental link between stored energy and mechanical stress.
Please read Section 2.1 'Introduction to SMES design' and Section 2.2 'Considerations about magnetic energy storage'. Focus on: The three main design objectives: mechanical integrity, maintaining the superconducting state, and maximizing specific energy. The statement of the Virial Theorem (Equation 3), which states that the stored energy E is directly proportional to the stress \sigma integrated over the volume of the support structure. The discussion of hoop stress in a solenoid, which is typically the largest and most critical stress component.
The Virial Theorem provides a stark conclusion: you cannot store large amounts of magnetic energy without an appropriately large and strong support structure. High energy density inevitably means high mechanical stress. Therefore, a major part of SMES design is structural mechanics, ensuring the winding and reinforcement can withstand the immense hoop stress.
3.3. Superconductor Choice and Operating Margin
The heart of a SMES is the conductor. Modern high-energy SMES exclusively use High-Temperature Superconductors (HTS), typically Rare-Earth Barium Copper Oxide (REBCO) tapes. While their critical temperature is high (~90 K), they are often operated at much lower temperatures (e.g., 20 K or 4.2 K) to achieve the highest possible current-carrying capability in the presence of strong magnetic fields.
The critical current of a REBCO tape is a strong function of temperature, the magnitude of the magnetic field, and the field's orientation relative to the tape surface. The coil designer must use Finite Element Analysis (FEA) to calculate the magnetic field at every point in the winding and ensure that the operating current remains safely below the local .
Superconducting Magnetic Energy Storage for Pulsed ...
The final design step is to select the conductor and ensure it remains superconducting under all operating conditions.
Please read Section IV, 'HTS CONDUCTOR FOR SMES COILS'. Notice how the designers first use FEA to find the maximum field in the coil (Fig. 10 and 11), then use that field value to determine the required amount of HTS tape needed to carry the target current with a safe operating margin (Fig. 12 and 13).
4. The Challenge of Protection
A SMES coil storing the energy equivalent of several kilograms of TNT must be protected against catastrophic failure. The most feared event is a quench—a sudden, irreversible loss of the superconducting state in a part of the coil. If this happens, the conductor becomes resistive, and the enormous stored energy begins to dissipate as heat () in that small volume, potentially melting or vaporizing the coil.
Protecting HTS-based SMES presents a unique challenge compared to traditional Low-Temperature Superconductors (LTS).
Superconducting magnetic energy storage and ...
The paper by Ciceron et al. concludes with an excellent discussion of the practical challenges in protecting a high-energy-density HTS coil.
Please read Section 2.7, 'Protection'. This is a critical section. Focus on: The description of a quench and thermal runaway. The difference in quench behavior between LTS and HTS (REBCO) tapes: LTS quenches propagate fast and are easy to detect; HTS quenches can be localized hotspots and propagate slowly, making them hard to detect before damage occurs. The resulting protection philosophy for HTS coils: use a large safety margin between the operating current and the critical current to make a quench event exceptionally unlikely in the first place.
Conclusion
In this lesson, we have explored the principles of Superconducting Magnetic Energy Storage as a sophisticated and highly efficient power source for pulsed magnets.
Key Takeaways:
- Principle: SMES stores energy in the magnetic field of a resistanceless superconducting coil ().
- Advantages: It offers high power density, rapid charge/discharge cycles, and extremely high energy recovery efficiency (>95%), making it ideal for repetitive pulsing.
- Operation: A Power Conditioning System (PCS) made of advanced power electronics manages the bidirectional energy transfer between the SMES coil and the magnet load.
- Design: SMES design is a multi-physics challenge involving optimizing coil geometry (e.g., Brooks coil), managing immense mechanical stresses (as dictated by the Virial Theorem), and selecting HTS conductors that can operate with a sufficient safety margin.
- Protection: Preventing and managing quenches is the primary safety challenge, and for stable HTS materials, this is primarily achieved by designing with a large margin to the critical current limit.
Next Lesson Preview:
We have now examined three major technologies for powering pulsed magnets: capacitor banks, inertial flywheel systems, and superconducting magnetic energy storage. In our next lesson, we will perform a systematic comparison of these different approaches, evaluating their respective strengths and weaknesses in terms of achievable peak field, pulse duration, cost, and experimental suitability. This will provide a comprehensive framework for selecting the right power source for a given scientific application.