Magnet Technology Beyond 50 T - IEEE Xplore

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Hans J. Schneider-Muntau, Andrew V. Gavrilin, and Charles A. Swenson. Abstract—The unique opportunities high magnetic fields offer scientific research, and ...
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Magnet Technology Beyond 50 T Hans J. Schneider-Muntau, Andrew V. Gavrilin, and Charles A. Swenson

Abstract—The unique opportunities high magnetic fields offer scientific research, and their use as a tool for science, have motivated many activities to expand their technological limits. Because of the Lorentz forces, the successful design of high field magnets is a challenge at the frontiers of magnet technology, and it is equally a stimulus for the materials scientist. The quest for higher fields translates into the urgent need for ultra-strong materials with higher Young’s modulus and conductivity. High field magnets are an ideal test bed for materials and concepts. Fields above 50 T can be generated with continuous and pulsed fields. We describe the technologies, which have been developed, the achievements and the potential for future improvements. We focus mainly on the field region between 50 T and 100 T. Index Terms—Continuous fields, high field magnets, high magnetic fields, pulsed fields.

I. INTRODUCTION AGNETIC fields are a very important tool for science. In fact, all efforts in generating the highest fields possible are driven by the desire and need to exploit them for experimental exploration of physical phenomena under extreme conditions, such as magnetic fields. Many publications, especially in condensed matter science, and several conferences are dedicated to this research area [1], [2]. We here focus on the generation of high magnetic fields beyond 50 T. One can distinguish four major technologies: a) continuous magnetic fields generated by superconducting, resistive and hybrid magnets up to about 60 T, b) pulsed magnets in the second to millisecond range up to 100 T, c) single turn coils, which generate fields in microseconds up to 300 T, and d) flux compression systems in the range of 600 T to 1000 T up to the record field of 2800 T. The highest continuous magnetic field generated today is 45 T [3]. It is routinely made available as a user facility at the NHMFL [4] with a hybrid magnet consuming 30 MW of electrical power. The step to 50 T is planned, and the development of a 60 T magnet has been recommended [34]. There is no principal limit to the generation of even higher continuous fields with resistive magnets; however power requirements soon become excessive because of insufficient strength and conductivity of the available conductors. Fields of this strength can rather easily be obtained with pulsed magnets during milliseconds. Only modest investments are necessary. Many universities have such a facility. Magnet technology above 50 T is dominated by the challenging task of

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Manuscript received September 19, 2005. This work was supported by the U.S. National Science Foundation under Grant DMR 0084173 and the State of Florida. The authors are with the National High Magnetic Field Laboratory (NHMFL), Tallahassee, FL 32310 USA (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TASC.2006.870844

handling the Lorentz forces. Design innovations to cope with the induced stresses, and the use of ultra-strong reinforcement materials within the winding, have pushed the limit to around 80 T [5]–[7]. Magnet longevity is limited because the conductors undergo heavy plastic deformation and cyclic strain hardening. These magnets are, therefore, an excellent test bed for new concepts and materials. Because of material limitations, 80 T [8] and 100 T [9], [10] two-coil magnets, energized by two energy storage systems, such as a 14 or 50 MJ capacitor bank or a 600 MJ generator, respectively, have been built or are in the planning or construction stage. At present, it appears impossible to generate fields above 100 T because of the lack of suitable materials. Material and design developments have been proposed to achieve 100 T in small coils [11]. Above 100 T the Lorentz forces are so strong, that the magnet necessarily explodes. The single turn system is a very elegant solution to this problem [12]–[14]. A very fast capacitor bank feeds current faster into the coil turn than that it expands, and the current flow continues in the vaporized exploding coil. Since the coil explodes symmetrically, the sample and its cryostat usually remain intact. Above 300 T can be generated by this technique during microseconds. Even higher fields are achieved by flux compression with electromagnetic fields [15] or explosives [16], [17]. Both systems require a seed field that is compressed by a collapsing liner. In the case of electromagnetic flux compression, a pulsed field generated by an additional outer coil induces strong current in a concentric liner, which compresses the seed field in microseconds. The world record of 2800 T has been achieved in Sarov, Russia, with a three-stage cascade system and 170 kg of explosives [18]. In the following chapter, we deal with continuous fields and explore the potential for producing fields above 50 T with superconducting, resistive and hybrid magnets. In the third chapter we describe and review in some detail the generation of magnetic fields up to 100 T with pulsed magnets with multi-turn, multi-layer coils. Because of the destructive nature of magnetic field generation above 100 T, and the negligible role magnet technology plays therein, we only touch on the single turn device and flux compression systems, both electromagnetic and with explosives. II. CONTINUOUS MAGNETIC FIELDS Fields above 50 T can be achieved, at least in principle, with superconducting and resistive magnets. For resistive magnets, there is no principal limit to the generation of highest continuous fields except for economics. Hybrid magnets consist of an outer superconducting magnet and an inner resistive magnet. The background or booster field of the superconducting magnet extends the field range of the resistive magnet considerably. Detailed information on the generation of continuous fields can be found in [19], [20].

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Resistive and hybrid magnets as they are made available at national user facilities are a cost effective alternative. B. Resistive and Hybrid Magnets

Fig. 1. Engineering current density of commercial conductors and of a prototype BiSCCO-2212 conductor. Courtesy of Oxford Instruments.

A. Superconducting Magnets The main advantage of superconducting magnets is their field quality and low operating cost. Measurements of extreme sensitivity can be performed. Temporal and spatial homo. In many research fields geneities can be improved up to superconducting magnets are used, such as condensed matter physics, and new research areas have been enabled, such as applications to ion cyclotron resonance and nuclear magnetic resonance. Resolving power, upper mass limit, peak coalescence and data acquisition time improve with higher fields for ICR, as do resolution and sensitivity for NMR experiments. As a result, there is a strong demand for higher fields. Present magnet technology is based on low temperature superconductors, which limits the fields to about 22 T (Fig. 1). Already in 1994, a feasibility study has been performed at the NHMFL to demonstrate the usefulness of high-temperature superconductors (HTS) for the generation of magnetic fields [21]. The use of HTS at low temperatures increases their current carrying capabilities dramatically and makes them a promising candidate for high field inserts. The highest field ever generated, both incrementally and absolutely, is the 5 T insert magnet built at the NHMFL. In the background field of a resistive magnet of 20 T, 25 T total field have been created. The insert alone can generate a self-field of 7.2 T [22]. Recently, first studies have been performed about a 30 T NMR magnet [23] demonstrating its feasibility. Measurements in the hybrid magnet at the NHMFL up to 45 T show a consistent behavior of HTS conductors, see Fig. 1 and [24]. It is fair to assume that the dependence of the critical current density on the magnetic field will continue with the same slope beyond 45 T to 50 T and even higher. This means that superconducting magnets with field strength of 50 T and beyond can be built. As expected, the Lorentz forces and the insufficient mechanical properties of the available conductors make the magnet enormous and unrealistic. First estimates performed at the NHMFL [25] indicate that such a system would have an outer diameter of 8 m and weigh close to 800 T. 90 % of the magnet volume is reinforcement, in this case high strength steel. For the generation of high fields, the development of conductors with high mechanical strength is, therefore, of utmost importance. Because of its size, cost will be prohibitive for standard applications.

In 1966, it has been estimated that 40 MW of power would be required to generate 33 T with a Bitter magnet [26]. Since then, energy effective magnet designs and better materials have been developed that generate magnetic fields up to 33 T with less than half the power (17 MW) [27]. Lorentz forces grow quadratically with the field. At higher fields it becomes, therefore, necessary to choose conductors with higher strength, which have a higher resistivity, i.e., consume more power. Above a certain field level it is more efficient to shift some of the field generation to outer, less stressed but also less efficient magnet regions. This means that with resistive magnets the deficiencies of the conductors can be overcome by building bigger magnets and applying higher power levels. Today, only two types of magnets are in use worldwide: the poly-helix magnet [28] and the Florida–Bitter magnet [29]. The word “polyhelix magnet” has been coined for a magnet system that consists of a set of thin monolayer coils that are mechanically independent. Their current distribution can be optimized under several constraints: hoop stress, temperature, homogeneity, or endforces [30]. The most dramatic improvement in cost and power efficient magnet design was the introduction of the radially compliant Bitter disk [29] by one of the authors. The compliance is achieved by placing long and curved cooling slits in a staggered pattern. The Florida–Bitter magnets have been developed to highly utilized research instruments at the NHMFL in Tallahassee. Because of their relatively cost efficient construction and reliability, other laboratories (Tsukuba, Japan [31] and Nijmegen, Netherlands [32] have adopted the design. The NHMFL hybrid magnet generates 45 T since of June 2000. The laboratory has plans to upgrade the superconducting magnet to 15 T, and the power supply to 48 MW. This will make it possible to produce continuous fields of at least 50 T. Based on the extensive experience available with the Florida Bitter magnet design, and a range of computer and optimization programs, it is possible to predict further possibilities and make reasonable extrapolations. Fig. 2 summarizes the results. Because of the Lorentz forces, and in spite of improved designs and the availability of better conductors, the basic quadratic relationship between power and magnetic field can only be maintained up to fields of about 20 T. As a rule of thumb, one can say that each increment of 10 T requires a doubling of the power resulting in an exponential increase of the power requirements with field. For hybrid magnets, the addition of a background field of the superconducting outsert does not translate into an equal increase of the total field. Typically, it is 50 % or even less. It is the result of the fact that the resistive magnet becomes less efficient because it experiences the booster field, and consequently, increased Lorentz forces. Equally important, the reduced space in the inner bore of the outsert has an impact on the radial current density distribution, which is far from optimal. Fig. 2 displays the result of all these effects. We conclude that 50 T should be feasible with a continuous power of about 40 MW and possibly 55 T with 60 MW. A background field magnet with

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Fig. 2. Magnetic field with bore size in mm as a function of power. Hybrid A and B are for hybrid outserts with 18 T, 1000 mm and 15 T, 600 mm inner diameter, respectively, showing the growing inefficiency of resistive and hybrid magnets. The dashed line indicates the present power level of the NHMFL, the dotted line the power available after upgrading.

a bore of 1000 mm instead of 600 mm and generating 18 T instead of 15 T could boost the field to 60 T requiring around 50 MW of power [33]. III. PULSED MAGNETS The main driver for the development of pulsed magnetic fields is the fact that they are relatively inexpensive and that they allow for easy access to fields in the 50 T region. A wealth of experimental results, mainly in solid state physics, has been achieved in these compact devices. Magneto-transport, high-field superconductivity, spectroscopy, fermiology, electron paramagnetic resonance, and recently nuclear magnetic resonance, are a few of the many research fields [1], [2]. Disadvantages of pulsed fields are short measuring times, eddy-current heating in conductive samples, induced voltages by the changing magnetic field, shocks and vibration of the magnet, and the occasional destruction of a magnet. Modern electronics can measure and store at extremely high repetition rate and resolution, and allow for signal treatment to subtract noise, induced and interfering voltages. There are more than 30 facilities around the world that develop and operate a wide variety of pulse magnets. Fig. 3 gives a summary of the available fields plotted against the pulse length [34]. It shows clearly that most laboratories produce 50–60 T, and that only very few achieve 70 T or even higher. Pulsed fields in the millisecond range are a cost effective and easy to use alternative to continuous fields. A facility requires an energy storage system, such as a capacitor bank, which is charged and then discharged via a thyristor, ignitron or spark gap into a magnet coil. The generation of pulsed fields is cost effective, as for approximately $200 k a complete laboratory can be installed, with about $100 k for a capacitor bank of 500 kJ, and $100 k for the scientific and data recording equipment. Magnetic fields up to 50 T can be generated rather easily, and there is the promise that fields up to 100 T can be produced with small but more sophisticated coils [11]. A pulsed magnet consists of several layers (typically between 8 and 12) with many turns per layer (20 or so). The magnet is

Fig. 3. Field strength and pulse duration of pulse magnets available at facilities worldwide. After [34].

immersed in a liquid nitrogen bath to pre-cool it. Because of the short discharge time, the magnet heats practically adiabatically. The heat capacity of the magnet determines the final temperature, which defines the minimum magnet volume as function of the dissipated energy. Roughly 100 kJ of energy heat 1 kg of . Pulse magnets are, therefore, small and conductor to 100 compact. Lorentz forces are the main challenge for the magnet designer. A simple model describes the magnetic field as pressure that creates the stress in a thin winding cylinder

It has been shown [35] that in thick coils, the stress distribution is more favorable. In this case the hoop stress is only about half of the magnetic pressure. The axial stress resulting from , the von Mises the radial field component adds about 3/16 . A 100 T magnet of this destress is therefore sign would require a conductor with yield strength of 2.4 GPa, far beyond of what is available today. This again underlines the importance of developing suitable conductors for the generation of higher magnetic fields. There are two main requirements for a high field conductor: high strength, and high conductivity. In first approximation, the conductor strength determines the maximum field and its conductivity, through the heating of the conductor, the pulse length. Other important characteristics are strain, fatigue life, impact strength, bending radius, dimensions, piece length, heat capacity, and equally important issues like availability and cost. The magnet requirements as a tool for research are, above all, reliability and repeatability in performance without degrading or electromagnetic noise. Maximum field, long pulses with not too short rise times and long decay times are desirable. After the pulse, the magnet has to be cooled again, a time during which the experiment idles. Short cool-down times are advantageous. Experience tells us that maximum field and user field are not identical. Because of the high degree of plastic deformation in tension during the pulse, and in compression after the

SCHNEIDER-MUNTAU et al.: MAGNET TECHNOLOGY BEYOND 50 T

pulse, the fatigue life of the conductor, and equally of the reinforcement and the insulation, is strongly reduced. In the interest of safe operation and maintenance of the research equipment and the sample, it is advisable to leave a safety margin of 5–10 %. Most user magnets can be categorized as either “short pulse” or “mid-pulse” designs. A short-pulse magnet system has a pulse duration between 5 ms and 50 ms (Fig. 3). The mid-pulse magnet systems typically have pulse durations between 50 ms and 1000 ms. Short pulse magnets are more suitable for high field operation since the shorter pulse length reduces the Joule heating integral, also called the “action integral”, in the conductor. A. Historical Perspectives It was in 1927 when for the first time a field strength of 35 T has been achieved [36]–[38]. Since then, pulsed fields with intensities up to 40 T have become common, using Cu conductor in coils with simple external reinforcement shells. A very reliable 40 T magnet technology was developed at the University of Amsterdam in the 1970’s [39]. The magnet was driven by a regulated power supply and different pulse shapes could be generated, such as a flat top of 100 ms. The first 50 T and 60 T fields have been achieved in Oxford with CuSS conductors [40] and multi-section coils using various wires [41]. Magnet development in Toulouse focused on mid-pulse coil technology with a milestone of 61 T for a 200 ms pulse width [35]. The application of reinforcement was limited to a single external shell common to earlier works. The principal development focused on the production of ultra high-strength high-conductivity wire to limit the plastic strain during operation [42]. Similar technical progress, in short pulse coils, had been made at MIT in 1986 using high-strength high-conductivity Cu-Nb conductor achieving a maximum field of 68.4 Tesla [43]. Work at ATT Bell Laboratories succeeded in a peak field of 72.6 Tesla [44] by grading conductor materials to adjust for the strain level. The concept of distributed internal reinforcement in short pulse magnets was developed and implemented in Leuven [45]. This concept is in analogy to the design schema developed for water cooled poly-helix magnets, where each layer supports itself and the space for cooling is used for reinforcement [28]. Internal reinforcement technology has been adopted by design groups at several pulsed field laboratories around the world. A most notable contribution is the work in Osaka with reported peak record fields of 82.3 T by including the use of maraging steel reinforcement shells with Cu-Ag conductors [6]. In the last years, two programs have been undertaken in Europe and the United States: the two stage “coilex-coilin” pulsed magnet system [46], and the large generator driven systems operated at NHMFL Pulsed Field Facility [47], [48]. The “coilex-coilin” pulsed magnet system evolved into the European ARMS (Advanced Research Magnet Systems) program. It has achieved 76 T pulses using a double power supply system where a 14 MJ capacitor bank powers a large bore 24 T outer “coilex” magnet, and a 250 kJ capacitor bank energizes a 49 T “coilin” or “insert” magnet with a 1.5 ms rise time [8]. The NHMFL has undertaken two major pulsed magnet programs utilizing the LANL generator system: the 60 T long pulse magnet

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generating quasi-continuous 60 T pulses with a 100 ms flat top [49], and the 100 T system. The rebuild of the 60 T magnet [50] is now nearing completion. Design and construction of the 100 T multi-shot pulse magnet is in progress. It will initially deliver 90 T pulses and utilize two power supply systems, a 2 MJ capacitor bank and the 1.4 GW/560 MW motor generator. The 2 MJ capacitor bank energizes a 50 T insert magnet with 5 ms rise time [51]. B. Development Path for Pulsed Magnets A thorough analysis of the achievements in the generation of pulsed fields and the intention of defining a development path to higher fields has resulted in several important insights. The NHMFL, being one of the youngest magnetic field laboratories, had the chance to review and analyze past activities in the beginning. This helped to establish a detailed understanding of the physics of pulsed magnets and develop a scientific basis for the envisaged approach. Six areas have been recognized as being crucial for the success: a) internal reinforcement, b) external reinforcement, c) detailed magnet analysis with computer codes and finite element (FE) calculations, d) materials characterization and development, e) optimization of magnet parameters and f) dynamic effects. 1) Internal Reinforcement: An analysis of the stress distribution of high field magnets reveals that radial stresses play a decisive role. The radial stress is tensile in the inner part and compressive in the outer part. It is, therefore, important to separate a magnet into two parts, which are characterized by the radius where the radial stress goes through zero. The inner layers will try to separate, and the design must be such that they can separate, and furthermore each layer has to be reinforced so that it withstands its Lorentz forces on its own. This means that internal reinforcement has to be introduced. The combination of Zylon with MP35N gives the desired result. 2) External Reinforcement: The outer layers support each other because the radial stress is compressive. External reinforcement is necessary to support these layers, which otherwise would yield. A combination of SS 301 and Zylon has proven to be adequate. Wire and layer insulation have to be tolerable to the radial pressure, and also to the axial pressure from the radial field component, which is highest somewhere at half of the outer radius. 3) Magnet Analysis: Pulsed magnets are very complicated systems with a high number of variables, which are partly interdependent and have a complex impact on field and longevity. It is, therefore, indispensable to have precise and detailed computer codes that calculate stresses, strains, temperatures, cycling, work hardening, etc., and allow for optimizing the different variables. They are also a very powerful tool to develop an understanding of the physics of the magnet by making Gedanken experiments possible. These codes assume rotational symmetry, and allow for precise optimization of the magnet lay-out. 3-D analysis of critical parts of the magnet is then performed by FE programs. Temperature distribution and a short cool-down time are also essential. Magnets can be optimized for equal heating during the pulse in spite of the different sources of energy dissipation: ohmic heating, eddy current heating, and magneto-resistance. They can also be

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optimized for equal cooling: an example is described in the next chapter. 4) Materials: As already mentioned, materials are the key issue in pulse magnet design. Their importance cannot be stressed enough. Pulsed magnet design, once optimized, is only limited by materials, and this is true for the conductor, the reinforcement and the insulation. The frontier between destructive and non-destructive fields, at present at about 100 T, is only a materials issue. We need stronger reinforcement materials with high yield strength and high Young’s modulus. We need insulation materials with better mechanical properties and especially strain tolerance, and we need better conductors. The NHMFL and other laboratories have stimulated , a dispersion industry to develop better conductors. strengthened conductor, and Cu-Nb, a microcomposite, have contributed to recent progress in high field generation. This potential has been explored and exhausted. A new generation of conductors is needed. Successful magnet design is also based on a perfect understanding of the behavior of the materials. At the NHMFL, and other laboratories, detailed characterization of the conductors and reinforcement materials takes place. Fatigue through cycling into compression (negative r values) and temperature impact are taken into account. Comprehensive data bases have been established. 5) Optimization of Magnet Parameters: Pulsed magnets are typically wound from one length of wire with an equal number of turns per layer. A rectangular coil cross-section with constant current density results. As demonstrated earlier with polyhelix [28] and poly-Bitter magnets [52], the performance of magnets can be drastically improved by changing the current density distribution in axial and radial direction under the constraints of stress and temperature, and higher field values can be achieved. For the case of a pulsed “polylayer magnet”, the following parameters can be optimized: choice of conductor strength and conductivity, width and height of the conductor of each layer, number of turns of each layer, choice of reinforcement, and thickness of the reinforcement of each layer. Of special importance is the interaction between conductor and layer reinforcement. Determined by their respective Young’s moduli, the optimum sharing of the Lorentz force is achieved when both are loaded to their maxima. Usually, however, the conductor is strain limited, and the reinforcement is stress limited. 6) Dynamic Effects: During a few milliseconds, the conductor in a pulse magnet is cycled from a pre-stressed state at 77 K to its maximum strength accompanied by a jump in temperature of about 50 K. During the next milliseconds it is relieved and goes into a compressive state while the heating continues to about 400 K. This is followed by a slow cooling process to 77 K. The impact of this cycling of stress and temperature on conductor performance is unknown. The same effects strain the reinforcement and the insulation. It is not inconceivable that layer transitions fail because of dynamic effects. Pulsed magnets are unique test beds for materials, and systematic studies should be performed. C. The Road to Higher Fields Based on what has been said above, simulation calculations of a polylayer magnet have been performed to investigate the de-

Fig. 4. Cross-section of an optimized 100 T polylayer magnet with 10 layers, table of conductor cross-sections and reinforcement thickness.

velopmental path future magnet technology should take [11]. It has been shown that 100 T can be achieved in rather small coils under two conditions: a) optimizing the current density distribution over the coil volume, and b) development of a specific conductor. As an example, the cross-section of a 100 T magnet and the conductor dimensions and the reinforcement thickness of each layer are displayed in Fig. 4. The magnet is dominated by reinforcement—charged to 4.1 GPa—underlining the need for stronger reinforcement materials. For the conductor, 900 MPa yield strength, 1780 MPa UTS, 128 GPa Young’s modulus and strain tolerance of up to 1.78 % had to be assumed. Two important conclusions can be drawn from this exercise: a) 100 T is at the borderline of what can be achieved today with small coils (10 mm bore, 2 MJ), and b) the development has to be directed towards conductors with high conductivity, and not high strength, as has been argued up to now. Both microcomposite (Ag-Cu) [53] and macrocomposite conductors should be developed. Integration of high-strength fibers, such as Zylon or M5, in the conductor seems promising and feasible. D. NHMFL Magnet Technology Several technological advancements have been made since beginning work at the NHMFL in 1991. A specialized pulsed magnet design code was developed [54], [55]. Precision machined G-10 transition filler blocks for layer to layer transitions, and Zylon & metal as a hybrid reinforcement structure with matched radial modulus were introduced [56]–[58]. A record field of 78.8 T was achieved in 1998 [7]. This magnet was “non-destructive” meaning that it did not disassemble during the peak field pulse. A new pulsed magnet design template was developed between 2001 and 2003 [59]. This engineering work entailed: 1) the improvement of layer-to-layer transition geometries within the windings, 2) the introduction of coaxial current leads to reduce noise, 3) the development of the “poly-layer” helix design and assembly process, 4) the implementation of free supported lead technology [60], 5) demonstration of fastcool technology [59], 6) introduction of Al-60 Glidcop as a conductor, and 7) co-development of large monolith Cu-Nb conductors with Bochvar Institute [61]. The first implementation of these developments was the NHMFL 65 T magnet system. The 65 T was a radical departure from the traditional coil designs based upon the Leuven technology at NHMFL. The 15 mm bore 65 T magnets are especially unique in that they are the first magnets with fast cooling technology (see Fig. 5) built as two series-connected

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Fig. 7. Field, current and field/current ratio of a single turn coil as function of time [62]. Fig. 5. Calculated evolution of the radial temperature distribution over the 65 T coil in the mid-plane. Maximum conductor temperature after a shot is 380 K. Inner and outer surfaces and gap are pool-cooled with LN .

coils. A cooling manifold was introduced between the inner and outer coils resulting in a thermal recovery time of only 24 min after a 65 T pulse. Fig. 5 illustrates the temperature profiles within the magnet assembly after a high intensity pulse. Since 2003 the 65 T series has delivered over 3642 pulses in three magnets. The development of these intermediate pulsed magnet systems provided an opportunity to cost effectively implement and test technology for the 100 T insert program [51]. The multiple engineering changes have been validated by improved performance and reliability (Fig. 6). The latest development, the NHMFL 75-T magnet system is notable in that it produces 75 T pulses with 5 ms rise time and about 15 ms total pulse width while using only 1.49 MJ of energy [5]. The technical development path is to produce 80 T prototypes as a performance limit study for the 100 T multi-shot magnet program.

turn coil (Fig. 7). Because of the enormous current density and Lorentz forces the coil expands, melts, vaporizes and explodes. The field that can be obtained is the result of the competition of the coil expansion, which reduces field, and the increase in current (B/I in Fig. 7). The capacitor bank must be faster than the thermal and mechanical inertia of the coil. Single turn pulses are, therefore, very short, typically a few microseconds. Since there is no discontinuity in the current flow during the explosion, it is assumed that the current continues to flow in the metal vapor of the vaporized coil. The explosion is directed radially outward. The beauty of the device is that, because of the symmetry of the coil expansion, sample, sample holder and cryostat remain intact. In addition, the magnetic field in the bore protects against intrusion of conducting matter. The symmetry of the discharge is, however, only maintained up to about 250 T. Above this field value the slit effect from the current feeds dominates with the consequence that metal vapor enters the bore, and the scientific set-up is destroyed. Because of the requirement of a fast discharge, the inductance of the whole system has to be as low as possible leading to the smallest magnet possible, a single turn coil. Furthermore, the inductance of the capacitor bank, the switches and current feeds have to be small, too, since the total inductance determines the current rise time, and the internal inductance reduces the output voltage. The same applies for the resistance of the coil and the system. An additional requirement for a fast discharge is small capacitance, which means high bank voltage. The switches, typically spark gaps, are of the rail gap type, and have very little jitter. Typical single turn devices have 60–75 kV, 100–200 kJ, and a total inductance of less than 20 nH. Single turn devices have been developed since many years, and the first system obtained 160 T [62]. The highest field ever achieved in a reinforced coil was 390 T [63]. Today, there are three facilities in continuous operation: in Kashiwa/Tokyo [12], Berlin [13] and Los Alamos [14]. Single turn devices are reliable research instruments. On average, one shot per hour is possible. The coils and current feeds, as indicated in Fig. 6, are mass produced from copper sheet.

IV. SINGLE TURN COIL

V. FLUX COMPRESSION

Single turn devices have extended the useful field range to above 311 T. The extremely high field is created by passing a current in the order of several MA through a small single

Compression of magnetic flux can be achieved electro-magnetically and with explosives. In both cases, a liner that contains the seed field is imploded. Since the liner is resistive, part of

Fig. 6. Operation record for 65 T P3. Data covers time period between November 2003 and August 2004.

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shells of densely packed insulated Cu wires. It has proven advantageous to have several of these liners in series, as they stabilize the captured flux, therefore the name “cascades” [68]. ACKNOWLEDGMENT The authors want to thank T. A. Painter, NHMFL, for technical support and important contribution. REFERENCES

Fig. 8. 28.4 kT, the highest magnetic field ever achieved. D: innermost liner diameter, Fi: flux containment, B: magnetic field. The connected dots are the experimental data, the others are results of calculations [18].

the flux diffuses out during the compression phase. The highest fields are achieved with explosive flux compression, however the nature of these experiments requires that they are made outside in a remote place, and the handling of explosives requires strict safety and security measures. A. Electromagnetic Flux Compression A flux compression experiment is performed in a shielded room, which protects the environment from acoustic and electromagnetic noise and expulsed fragments. A flux compression device consists of an outer single turn coil that provides the compression field, a set of coils for the seed field, and the liner. The liner is from annealed copper. The high dB/dt of the outer coil induces strong currents in the liner, which in interaction with the outer field implodes the liner. The maximum field that can be achieved depends on the initial speed of the liner, but also on its compressibility and especially on the symmetry of the flux confinement. The feed gap effect could be reduced by the insertion of a thick-walled Cu cylinder, slitted in axial direction to allow for flux penetration [64]. The electromagnetic flux compression was first introduced in 1966 in the U.S. [65]. Today only one facility entertains a scientific user program, located in Kashiwa, Japan [66] providing fields up to 611 T. B. Flux Compression with Explosives Originally, flux compression experiments were developed for military research, and the results were classified. Today, standard experiments are performed in the 1000 T range, both at Los Alamos, U.S., (“DIRAC Series”) [16] and Sarov, Russia “KAPITZA Series” [68]. The world record has been achieved in Sarov with 28,400 T (Fig. 8) [18]. An experiment with explosives consists essentially of an internal volume of typically 100–175 mm diameter, filled with a seed field of about 10–20 T, up to three liners at different radii and an outer shell of explosives of up to 225 mm thickness. Precise ignition of the explosives is necessary to assure symmetric propagation of the detonation wave. The ingenious idea developed in Arzamas-16, now Sarov, is the use of liners, which are transparent to flux changes but fuse to a solid liner once the shockwave from the compression has hit them. They consist of

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