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High magnetic fields
Journal of Magnetism and Magnetic Materials 6 (1977) 3-6 © North-Holland Publishing Company
HIGH MAGNETIC FIELDS E. BRAUN Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-3300 Braunschweig, FederalRepublic of Germany Received 9 April 1977
This paper givesa short summary of today's commonly used methods of producing and measuring high magnetic fields.
1. Introduction
2.1. Bitter magnets
During the period that superconducting magnets had not yet been developed, it became common to call magnetic fields above 3 - 4 T "high fields" because their production depended on technical effort exceeding the usual laboratory equipment [1-6]. For economical reasons in the past decades central laboratories for the production of high magnetic fields have been built in various places giving interested scientists the opportunity to experiment in stationary fields up to 25 T. Higher fields up to about 1000 T are, at present, only producible by pulse methods.
In 1936, F. Bitter [8] developed a method of producing magnetic fields higher than those of iron magnets. This construction, which has been named after him, consists of a pile of radial slitted copper plates, separated by isolating plates. The resulting distribution of the current in this kind of coil is inversely proportional to the rad'ius. Since nearly all of the input energy results in a heating of the coil, these plates have holes or channels, the size and position of which are carefully computed, optimizing the current distribution and the cooling effect. Usually an axial or radial flow of water at high pressure is used. These Bitter magnets have been built with an axial or radial access for the experiments. A typical Bitter magnet has, for example, in a 5 cm axial bore, a maximum field of 15 T consuming 5 MW power. Most of the high magnetic field laboratories have this kind of Bitter magnet. Laboratories with the facility to produce more than I0 T with power supplies of at least 2 MW at present exist at Braunschweig (Hochmagnetfeldanlage); Cambridge, Mass. (Francis Bitter National Magnet Laboratory, MIT); Grenoble (Service National des Champs Intenses); Malvern (Royal Radar Establishment); Moscow (Kurchatcvand Lebedev-Institute); Oxford (Clarendon Labortory); Saclay (CEA); Sendal (Tohoku University); Washington (Naval Research Laboratory) and Wroclaw. In a Bitter magnet consisting of several concentric coils, fields of up to 23 T have been produced at the Francis Bitter National Magnet Laboratory in Cambridge (USA).
2. Methods of producing high magnetic fields As long as the magnetic field is produced in a coil with finite resistance, the maximum induction in the symmetry centre of the coil is given by a formula which was evaluated already in 1898 by Fabry [7]: B = u o a (NX/pa) 1/~ ,
where G depends on the geometry of the coil and the current distribution in it, Nis the maximum available power, ?, is the ratio of space filled with conductive material to the available space, p is the specific resistivity of the conductor, and a is the radius of the bore of the coil. It will be shown that different types of magnets have been developed in order to optimize these numbers.
(1)
4
E. Braun /High magneticfields
The upper limit of the field which can be produced by Bitter magnets is given by the mechanical stresses caused by the forces between current and field, but the problems due to the necessary high power input are also increasing.
2.2. Cryoresist~'ve coils Attempts to lower the necessary power [cf. eq. (1)] by drastically lowering the resistivity of the conductor were made long ago. The temperature of aluminium coils has been lowered by cooling with liquid neon. It turned out that the total effort, including power supply and cryogenics, did not appear to be too drastic compared to coils operated at room temperature. Set-ups which operated with transient fields resulted in repetition rates of hours which were unfavourable for many of the experiments.
2. 3. Helix-coils Another possibility for using existing power suppries for the production of higher fields than those obtainable with Bitter coils, is to optimize the factor G in eq. (1) representing the geometry and current distribution of the coil. This leads to a coil consisting of concentric single-layered coils with different current and sometimes of different heights. These coils are called helix-coils or more accurately, polyhelixcoils. However, one has to take into account a much more complicated construction method, since the single coils have to be electrically isolated and very strongly mechanically compounded. The cooling problem still exists. A coil of this type which is supposed to give 25 T using the 10 MW power supply [9], has been developed in Grenoble.
2.4. Quasi-stationary fields Besides the pulsed field producing methods with fields lasting only milli- or even micro-seconds, which will be discussed later, some laboratories have built facilities ot produce fields which are reached in seconds, or last for this length of time. In Canberra, for example, a total energy of 580 MJ, stored in a homopolar generator, is used to produce 30 T in a magnet consisting of a Bitter coil and an inner helix-coil [10]. On the other hand, in Toulouse, success has been
achieved in prolonging the descent of a 40 T field obtained by discharging a condenser bank of 1 MJ to one second [11].
2.5. Superconducting coils in the meantime, it has been possible to obtain fields of up to 17.5 T by superconducting coils [12]. This special magnet consists of two concentric coils, the outer one made of NbaSn, and the inner one with a bore of 31 mm of V3Ga. Plans to construct a 20 T superconducting coil already exist [13]. Besides this, the time of ascent of the maximum field of the superconducting magnet has been lowered to about 3 min [14]. Thus, the superconducting magnets in the field range of up to 15 T will probably replace the Bitter magnets in the near future, also in respect to the consumption of power [15, 16]. The power supplies installed at the magnet laboratories can then be used to produce fields up to 30 T in so-called hybrid magnets.
2. 6. Hybrid magnets Since magnetic fields can be superimposed, it is possible to put a Bitter or a helix-magnet inside a sufficiently large bore of a superconducting magnet. This construction, which is called a hybrid magnet, is not in stable mechanical equilibrium, and the destructive forces have to be considered and overcome very carefully. In such a magnet, 25 T have been reached at the Kurchatov Institute in Moscow. The Clarendon Laboratory has a 15 T hybrid magnet. At the MIT Laboratory, a hybrid magnet has been completed for the University of Nijmegen which produces with a power of 600 MW 25.4 T. The MIT is building its own hybrid magnet designed for 30 T. Together with the ambition to produce record stationary fields, economical considerations also lead to the construction of hybrid magnets, because magnetic fields achieved only with Bitter magnets at present can be obtained with less power and more magnets can be run simultaneously.
2. 7. Transient fields To produce fields higher than 25 or 30 T, galvanic, capacitive, inductive or mechanical stored energy is discharged briefly in single- or multiple-turned coils
E. Braun / High magneticfields [17-19]. To produce fields higher than 75 T, the magnetic fluxes in these coils are compressed either by electromagnetic forces or by explosives (Cnareeffect [20]). Since the flux stays almost constant, the field is increased by the same amount by which the area is restricted. The disadvantage of these methods is the destruction of the sample. Nevertheless, Miura et al. [21] have done cyclotron resonance experiments in different semiconductors in fields of up to 150 T. One has to bear in mind that the density of the energy in the magnetic field which is proportional to B 2 reaches very high values at these so-called "Megagauss fields". At 130 T, for instance, the density of the energy has the same value as in the explosive TNT.
3. Methods of measuring high magnetic fields A great number of different methods have been developed [22-25], of which the following are commonly used.
3.1. Nuclear magnetic resonance The measurement of the precession frequency of the magnetic moment of a nucleus with a known gyromagnetic ratio (e.g. H +, H 2+, 27A1, and others) in a magnetic field gives an accuracy of 1 0 - 4 - 1 0 - 6 [26, 27]. To use this method, the homogeneity of the magnet has to be sufficiently high. Since the method requires some effort, it is often used to calibrate other field sensors.
3.2. Induced voltage The induced voltage proportional to the change of flux with time is measured. The change of flux in stationary fields is obtained by flipping, rotating, vibrating or translating of a coil. The accuracy is better than,0.1%.
3.3. Hall voltage The Hall voltage in semiconductors perpendicular to the current and perpendicular to the field is measured. The probe has to be adjusted very carefully perpendicular to the field. The Hall voltage is
5
not linear with the field, and is temperature dependent. Recent results of Rubin et al. [28] with commerical probes in fields up to 23 T have shown that the obtainable accuracy is better than 1%. If one also uses the reproducible deviations at low temperatures (Shubnikov-De Haas quantum oscillations) and with a dependence on the number of thermal cyclings, an accuracy of better than 0.2% is obtainable.
3.4. Magnetoresistance The magnetoresistance of metals (e.g. Cu) and of semiconductors (e.g. InSb, InAs, InSb-NiSb) is measured. The dependence of the resistance on the magnetic field can often be described by an exponential law [29]. This method has the advantage of a high reproducibility. The obtainable accuracy is up to 0.1%. The strong temperature dependence has to be borne in mind.
3.5. Faraday rotation The rotation of the plane of polarization caused by a material with known Verdet constant, which depends on the applied magnetic field, is measured. This method is often used in combination with the inductive method in extremely high fields [30].
References
[1] N. Kurti, Colloq. Int. CNRS No. 242,(1975) 15. [2] H. Brechna, Superconducting Magnet Systems (Springer,
Berlin, Heidelberg, New York, 1973). [3] H. Kuckuck, Phys. Z. 3 (1972) 131. [4] H. Kuckuck, Fachberichte der 35. Physikertagung (Hannover, 1970) p. 196. [5] Ch. Schwink, Z. Angew. Phys. 17 (1964) 131. [6] H. Kolm, B. Lax, F. Bitter and R. Mills, Prec. of the Int. Conf. on High Magnetic Fields, Cambridge, Mass. USA, 1961 (HIT Press and J. Wiley and Sons,lnc., New York, 1962). [7] C. Fabry, Eclair. Eleetr. 17 (1898) 133. [8] F. Bitter, Rcv. Sei. Instrum 7 (1936) 479,482; 8 (1937) 318; 10 (1939) 373. [9] H.-J. Schneider-Munthau and P. Rub, Colloq. Int. CNRS no. 242 (1975) 161. [10] P.O. Carden, J. Phys. E 5 (1972) 654,657,663. [11] S. Askenazy, G. Catrere and J. Marquez, Colloq. Int. CNRS no. 242 (1975) 357. [12] Phys. Today 29 (1976) 19.
6 [13] [ 14 ] [15] [16]
[17] [18] [19] [20] [21 ]
E. Braun /High magnetic fields P.S. Swartz, Int. Conf. of Magnetism, 1976, Amsterdam. P.S. Swartz, private communication. P.A. Hudson and H. Jones, Cryogenics 16 (1976) 593. J.D. Clement, private communication (at the NRL in Washington, D.C., the existing Bitter magnets will be supplemented by a superconducting magnet with a room temperature bore of about 5 cm and a maximum field of 15 T). H. Knoepfel and R. Luppi, J. Phys. E5 (1972)1133. C.M. Fowler, Science 180, (1973) 261. D. Schneider and J. Salge, Z. Angew. Phys. 31 (1971) 346. E.C. Cnaxe, J. Appl. Phys. 37 (1966) 3812. N. Miura, G. Kido, K. Suzuki and S. Chikazumi, Lecture Notes, Int. Conf. Appl. of High Magnetic Fields in Semicond. Phys. (Wtirzburg, 1976) p. 441.
[22] D.I. Gordon, R.E. Brown and J.F. Haben, IEEE Trans. Magn. 8 (1972) 48. [23] J.K.D. Verma, V. Raju and M.D. Aggarwal, Nucl. Instrum. Methods 104 (1972) 545. [24] C. Germain, Nucl. Instrum. Methods 21 (1963) 17. [25] J.L. Symonds, Rep. Progi. Phys. 18 (1955) 83. [26] F. Hartmann, IEEE Trans. Magn. 8 (1972) 66. [27] H. Br6mer, Lecture Notes, Int. Summer School on the Generation of High Magnetic Fields and their Application in Sol. Phys. (Wtirzburg, 1972) p. 404. [28] L.G. Rubin, D.R. Nelson, and H.H. Sample, Rev. Sci. Instrum. 46 (1975) 1624. [29] G.B. Scott, M. Springford and J.R. Stockton, J. Phys. E1 (1968) 925. [30] N. Miura, G. Kido, I. Oguro and S. Chikazumi, Colloq. Int. CNRS no. 242 (1975) 345.
HIGH MAGNETIC FIELDS E. BRAUN Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-3300 Braunschweig, FederalRepublic of Germany Received 9 April 1977
This paper givesa short summary of today's commonly used methods of producing and measuring high magnetic fields.
1. Introduction
2.1. Bitter magnets
During the period that superconducting magnets had not yet been developed, it became common to call magnetic fields above 3 - 4 T "high fields" because their production depended on technical effort exceeding the usual laboratory equipment [1-6]. For economical reasons in the past decades central laboratories for the production of high magnetic fields have been built in various places giving interested scientists the opportunity to experiment in stationary fields up to 25 T. Higher fields up to about 1000 T are, at present, only producible by pulse methods.
In 1936, F. Bitter [8] developed a method of producing magnetic fields higher than those of iron magnets. This construction, which has been named after him, consists of a pile of radial slitted copper plates, separated by isolating plates. The resulting distribution of the current in this kind of coil is inversely proportional to the rad'ius. Since nearly all of the input energy results in a heating of the coil, these plates have holes or channels, the size and position of which are carefully computed, optimizing the current distribution and the cooling effect. Usually an axial or radial flow of water at high pressure is used. These Bitter magnets have been built with an axial or radial access for the experiments. A typical Bitter magnet has, for example, in a 5 cm axial bore, a maximum field of 15 T consuming 5 MW power. Most of the high magnetic field laboratories have this kind of Bitter magnet. Laboratories with the facility to produce more than I0 T with power supplies of at least 2 MW at present exist at Braunschweig (Hochmagnetfeldanlage); Cambridge, Mass. (Francis Bitter National Magnet Laboratory, MIT); Grenoble (Service National des Champs Intenses); Malvern (Royal Radar Establishment); Moscow (Kurchatcvand Lebedev-Institute); Oxford (Clarendon Labortory); Saclay (CEA); Sendal (Tohoku University); Washington (Naval Research Laboratory) and Wroclaw. In a Bitter magnet consisting of several concentric coils, fields of up to 23 T have been produced at the Francis Bitter National Magnet Laboratory in Cambridge (USA).
2. Methods of producing high magnetic fields As long as the magnetic field is produced in a coil with finite resistance, the maximum induction in the symmetry centre of the coil is given by a formula which was evaluated already in 1898 by Fabry [7]: B = u o a (NX/pa) 1/~ ,
where G depends on the geometry of the coil and the current distribution in it, Nis the maximum available power, ?, is the ratio of space filled with conductive material to the available space, p is the specific resistivity of the conductor, and a is the radius of the bore of the coil. It will be shown that different types of magnets have been developed in order to optimize these numbers.
(1)
4
E. Braun /High magneticfields
The upper limit of the field which can be produced by Bitter magnets is given by the mechanical stresses caused by the forces between current and field, but the problems due to the necessary high power input are also increasing.
2.2. Cryoresist~'ve coils Attempts to lower the necessary power [cf. eq. (1)] by drastically lowering the resistivity of the conductor were made long ago. The temperature of aluminium coils has been lowered by cooling with liquid neon. It turned out that the total effort, including power supply and cryogenics, did not appear to be too drastic compared to coils operated at room temperature. Set-ups which operated with transient fields resulted in repetition rates of hours which were unfavourable for many of the experiments.
2. 3. Helix-coils Another possibility for using existing power suppries for the production of higher fields than those obtainable with Bitter coils, is to optimize the factor G in eq. (1) representing the geometry and current distribution of the coil. This leads to a coil consisting of concentric single-layered coils with different current and sometimes of different heights. These coils are called helix-coils or more accurately, polyhelixcoils. However, one has to take into account a much more complicated construction method, since the single coils have to be electrically isolated and very strongly mechanically compounded. The cooling problem still exists. A coil of this type which is supposed to give 25 T using the 10 MW power supply [9], has been developed in Grenoble.
2.4. Quasi-stationary fields Besides the pulsed field producing methods with fields lasting only milli- or even micro-seconds, which will be discussed later, some laboratories have built facilities ot produce fields which are reached in seconds, or last for this length of time. In Canberra, for example, a total energy of 580 MJ, stored in a homopolar generator, is used to produce 30 T in a magnet consisting of a Bitter coil and an inner helix-coil [10]. On the other hand, in Toulouse, success has been
achieved in prolonging the descent of a 40 T field obtained by discharging a condenser bank of 1 MJ to one second [11].
2.5. Superconducting coils in the meantime, it has been possible to obtain fields of up to 17.5 T by superconducting coils [12]. This special magnet consists of two concentric coils, the outer one made of NbaSn, and the inner one with a bore of 31 mm of V3Ga. Plans to construct a 20 T superconducting coil already exist [13]. Besides this, the time of ascent of the maximum field of the superconducting magnet has been lowered to about 3 min [14]. Thus, the superconducting magnets in the field range of up to 15 T will probably replace the Bitter magnets in the near future, also in respect to the consumption of power [15, 16]. The power supplies installed at the magnet laboratories can then be used to produce fields up to 30 T in so-called hybrid magnets.
2. 6. Hybrid magnets Since magnetic fields can be superimposed, it is possible to put a Bitter or a helix-magnet inside a sufficiently large bore of a superconducting magnet. This construction, which is called a hybrid magnet, is not in stable mechanical equilibrium, and the destructive forces have to be considered and overcome very carefully. In such a magnet, 25 T have been reached at the Kurchatov Institute in Moscow. The Clarendon Laboratory has a 15 T hybrid magnet. At the MIT Laboratory, a hybrid magnet has been completed for the University of Nijmegen which produces with a power of 600 MW 25.4 T. The MIT is building its own hybrid magnet designed for 30 T. Together with the ambition to produce record stationary fields, economical considerations also lead to the construction of hybrid magnets, because magnetic fields achieved only with Bitter magnets at present can be obtained with less power and more magnets can be run simultaneously.
2. 7. Transient fields To produce fields higher than 25 or 30 T, galvanic, capacitive, inductive or mechanical stored energy is discharged briefly in single- or multiple-turned coils
E. Braun / High magneticfields [17-19]. To produce fields higher than 75 T, the magnetic fluxes in these coils are compressed either by electromagnetic forces or by explosives (Cnareeffect [20]). Since the flux stays almost constant, the field is increased by the same amount by which the area is restricted. The disadvantage of these methods is the destruction of the sample. Nevertheless, Miura et al. [21] have done cyclotron resonance experiments in different semiconductors in fields of up to 150 T. One has to bear in mind that the density of the energy in the magnetic field which is proportional to B 2 reaches very high values at these so-called "Megagauss fields". At 130 T, for instance, the density of the energy has the same value as in the explosive TNT.
3. Methods of measuring high magnetic fields A great number of different methods have been developed [22-25], of which the following are commonly used.
3.1. Nuclear magnetic resonance The measurement of the precession frequency of the magnetic moment of a nucleus with a known gyromagnetic ratio (e.g. H +, H 2+, 27A1, and others) in a magnetic field gives an accuracy of 1 0 - 4 - 1 0 - 6 [26, 27]. To use this method, the homogeneity of the magnet has to be sufficiently high. Since the method requires some effort, it is often used to calibrate other field sensors.
3.2. Induced voltage The induced voltage proportional to the change of flux with time is measured. The change of flux in stationary fields is obtained by flipping, rotating, vibrating or translating of a coil. The accuracy is better than,0.1%.
3.3. Hall voltage The Hall voltage in semiconductors perpendicular to the current and perpendicular to the field is measured. The probe has to be adjusted very carefully perpendicular to the field. The Hall voltage is
5
not linear with the field, and is temperature dependent. Recent results of Rubin et al. [28] with commerical probes in fields up to 23 T have shown that the obtainable accuracy is better than 1%. If one also uses the reproducible deviations at low temperatures (Shubnikov-De Haas quantum oscillations) and with a dependence on the number of thermal cyclings, an accuracy of better than 0.2% is obtainable.
3.4. Magnetoresistance The magnetoresistance of metals (e.g. Cu) and of semiconductors (e.g. InSb, InAs, InSb-NiSb) is measured. The dependence of the resistance on the magnetic field can often be described by an exponential law [29]. This method has the advantage of a high reproducibility. The obtainable accuracy is up to 0.1%. The strong temperature dependence has to be borne in mind.
3.5. Faraday rotation The rotation of the plane of polarization caused by a material with known Verdet constant, which depends on the applied magnetic field, is measured. This method is often used in combination with the inductive method in extremely high fields [30].
References
[1] N. Kurti, Colloq. Int. CNRS No. 242,(1975) 15. [2] H. Brechna, Superconducting Magnet Systems (Springer,
Berlin, Heidelberg, New York, 1973). [3] H. Kuckuck, Phys. Z. 3 (1972) 131. [4] H. Kuckuck, Fachberichte der 35. Physikertagung (Hannover, 1970) p. 196. [5] Ch. Schwink, Z. Angew. Phys. 17 (1964) 131. [6] H. Kolm, B. Lax, F. Bitter and R. Mills, Prec. of the Int. Conf. on High Magnetic Fields, Cambridge, Mass. USA, 1961 (HIT Press and J. Wiley and Sons,lnc., New York, 1962). [7] C. Fabry, Eclair. Eleetr. 17 (1898) 133. [8] F. Bitter, Rcv. Sei. Instrum 7 (1936) 479,482; 8 (1937) 318; 10 (1939) 373. [9] H.-J. Schneider-Munthau and P. Rub, Colloq. Int. CNRS no. 242 (1975) 161. [10] P.O. Carden, J. Phys. E 5 (1972) 654,657,663. [11] S. Askenazy, G. Catrere and J. Marquez, Colloq. Int. CNRS no. 242 (1975) 357. [12] Phys. Today 29 (1976) 19.
6 [13] [ 14 ] [15] [16]
[17] [18] [19] [20] [21 ]
E. Braun /High magnetic fields P.S. Swartz, Int. Conf. of Magnetism, 1976, Amsterdam. P.S. Swartz, private communication. P.A. Hudson and H. Jones, Cryogenics 16 (1976) 593. J.D. Clement, private communication (at the NRL in Washington, D.C., the existing Bitter magnets will be supplemented by a superconducting magnet with a room temperature bore of about 5 cm and a maximum field of 15 T). H. Knoepfel and R. Luppi, J. Phys. E5 (1972)1133. C.M. Fowler, Science 180, (1973) 261. D. Schneider and J. Salge, Z. Angew. Phys. 31 (1971) 346. E.C. Cnaxe, J. Appl. Phys. 37 (1966) 3812. N. Miura, G. Kido, K. Suzuki and S. Chikazumi, Lecture Notes, Int. Conf. Appl. of High Magnetic Fields in Semicond. Phys. (Wtirzburg, 1976) p. 441.
[22] D.I. Gordon, R.E. Brown and J.F. Haben, IEEE Trans. Magn. 8 (1972) 48. [23] J.K.D. Verma, V. Raju and M.D. Aggarwal, Nucl. Instrum. Methods 104 (1972) 545. [24] C. Germain, Nucl. Instrum. Methods 21 (1963) 17. [25] J.L. Symonds, Rep. Progi. Phys. 18 (1955) 83. [26] F. Hartmann, IEEE Trans. Magn. 8 (1972) 66. [27] H. Br6mer, Lecture Notes, Int. Summer School on the Generation of High Magnetic Fields and their Application in Sol. Phys. (Wtirzburg, 1972) p. 404. [28] L.G. Rubin, D.R. Nelson, and H.H. Sample, Rev. Sci. Instrum. 46 (1975) 1624. [29] G.B. Scott, M. Springford and J.R. Stockton, J. Phys. E1 (1968) 925. [30] N. Miura, G. Kido, I. Oguro and S. Chikazumi, Colloq. Int. CNRS no. 242 (1975) 345.