- Email: [email protected]
The exploding wire phenomenon
Volume 107A, number 5
PHYSICS LETTERS
4 February 1985
THE EXPLODING WIRE PHENOMENON H. ASPDEN
Department of Electrical Engineering, University of Southampton, Highfield, Southampton S09 5NH, UK Received 4 October 1984 Revised manuscript received 21 November 1984
Graneau's recent interpretation of the exploding wire phenomenon as an electrodynamic effect verifying Amp6re's classical formulation is questioned. Instead, it is shown that the rupturing force arising from the imbalance of the self-induced electromotive force and the ohmic potential during an explosive current surge will account for the wire breaking into several segments, as is observed.
Graneau [1 ] has recently drawn attention to the phenomenon by which very high currents suddenly applied to a thin conducting wire cause it to explode into several small elements as if subjected to tensile fracture forces which cause the wire to rupture before becoming unduly softened by the ohmic heating. His experiments confirm the earlier findings of Nasilowski [2] by which the wire explosion was permanently arrested to leave wire fragments o f undiminished diameter with fracture faces very nearly perpendicular to the wire axis. Graneau offers a theoretical explanation for this hitherto unexplained phenomenon, basing his argument on the axial forces expected to exist between separate elements of a current circuit according to A m p ~ r e - N e u m a n n electrodynamics as they apply to steady currents. This is in spite o f the rigorous mathematical requirement o f classical electrodynamics that if a current filament is truly circuital the mutual electrodynamic action between an element and the remainder o f the circuit must, on established empirical evidence, involve only forces perpendicular to current flow in that element. Graneau effectively specifies an open circuit condition by which isolated circuit elements are subject to axial forces generated by mutual action o f current in different parts o f the element. The force is o f the form i21og(L/D), where i is the current in absolute amperes and L/D is the ratio of the length o f the element L to a quantity D of the order o f its 238
thickness. With LID equal to 2 000, this gives a tension of 7.6 kg for a current of 10 000 A, which Graneau notes as sufficient for breaking a 1.5 m long copper wire of 1 mm diameter, severely weakened by Joule heating. He justifiably discounts the pinch forces which analysis shows as generating a radial pressure on the surface of the wire corresponding to an axial force of the order o f i2/2. Such forces are too small to cause rupture showing clean tensile fracture. Graneau's emphasis upon the fact that the fractures are tensile in character, whereas pinch forces are compressive and could not cause wire fragmentation of the form observed, can be questioned in the light of experimental research by Bridgman [3]. The application of compressive forces to the cylindrical surface of a rod specimen can cause fracture even though there is no longitudinal stress. Bridgman's surprise at the form of the fracture is clear. He commented "the rupture looks very much like that of a tensile break". More important, however, in challenging Graneau's theoretical account, is the assessment of the magnitude o f the force needed to rupture the wire, particularly as it is not explained why the wire breaks into as many as 50 fragments. Each of these fragments is of insufficient length (far less than 1.5 m) to develop adequate force according to the Graneau method o f calculation. Though in a later paper Graneau [4] discusses the multiple rupturing o f the wire in terms of a progressive weakening o f the residual wire segments with increase 0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 107A, number 5
PHYSICS LETTERS
in temperature, it is felt that an alternative explanation should be sought for this quite remarkable phenomenon. The most obvious cause for an axial force in the path of current flow is the direct action of electromotive force on charge in the conductor. When an emf is applied to a conductor the field intensity E applies force to the electron population having the mobility which accounts for current flow. The forces impart momentum to the electrons which is transferred by collision to the atomic lattice of the conductor. The collision forces are balanced by the action of E upon the positive charge of this atomic lattice. Overall, there is no resultant axial force on the conductor because the emf and the potential drop determined by the collisionrelated ohmic losses are in balance. Thus, in the steady state current condition, the closed circuital flow involves no axial forces along the current path. Now, when the emf is changing owing to magnetic induction effects, including self-induction within the conductor, the applied emf and the potential drop are no longer in balance. Their difference can be measured experimentally and can account for an axial force in the line of current flow [5]. Under these conditions the positive atomic lattice o f the conductor is subject to the full intensity E, as are the electrons, but the electrons have an additional role. They act as a catalyst in transferring momentum to the lattice by collisions, but they also transfer momentum to whatever it is that acts as the store for the energy associated with the magnetic induction process. The field medium is closely coupled with the collective electron action and this field can assert forces in its interaction with charge in matter. In effect, therefore, we can reasonably expect a residual axial reaction force corresponding to the work done by the emf in feeding energy into the selfinductance of the conductor when its current increases. The force will be an axial force acting between the conductor and the field induced in the observer's reference frame by the electron motion. Such a force can cause rupture of the conductor if the current build-up is rapid enough, but it cannot separate the conductor body from the electron population owing to their strong electric coupling. All that can be expected is that the conductor will disintegrate into elements which are contained during the explosion within the plasma formed by the current discharge. The reason for this is that the force acting on each
4 February 1985
positive element of the atomic lattice of the conductor will not, in general, be the same throughout the conductor. The rigidity and internal cohesion of the conductor will determine if it is to withstand the rupturing forces resulting from its inertial reaction with several parts accelerating at different rates. This is the situation (a) if the test conductor is not a perfectly straight specimen so that axial forces in adjacent segments pull in different directions and, more likely, (b) if the current discharge is unstable along its length, as exemplified by the snaking of discharges in high current fusion research, so that, though centred by the conductor chan. nel, some of the flow arcs into surrounding plasma and is not wholly confined to the body of the conductor but asserts forces concentrated on segments spaced along its length. The quantitative analysis fully supports this explanation. The self-inductance of a filamentary conductor is 5 × 10-10 H/cm (see ref. [6]). If a current of the form 10 sin cot amperes flows in this conductor it will develop an emf related to self-inductance and given by 10w cos cot times 5 × 10-10 V/cm. This is an electric field amplitude of 1.67 × 10 - 1 2 t i m e s I 0 w when measured in esu volts per cm. The free electron population in an aluminium conductor is, according to Ehrenberg [7], 2.1 X 1023 per cc and, since electron charge is 4.8 × 10-10 esu, we see that the total atomic lattice charge density balancing the free electron population is about 1014 esu per cc. The action of the electric field on this charge density produces a mechanical force given by 167 (low) dyne c m - 2 per cm length of conductor. In Graneau's experinaent the value o f I 0 was 5 000 A and it was supplied through an inductor by discharging a capacitor bank. The wire exploded as the current oscillated for a few cycles at 2 000 Hz. Thus w was 12 566 and 167 (I0w) then becomes 1.05 X 1010. It follows that our theory requires the aluminium wire used by Graneau in his experiments to be subject to a transient tensile stress of up to 1.05 × 1010 dyne c m - 2 for each cm length of conductor carrying the 5 000 A current. The tensile strength of aluminium depends upon the purity of the material and the manner in which the metal is worked. Reference data [8] quote the tensile strength as 4.74 × 108 dyne cm - 2 for annealed wrought aluminium of high purity and 11.2 × 108 dyne c m - - - f o r the same when cold rolled. However, if the aluminium wire used by Graneau was an 239
Volume 107A, number 5
PHYSICS LETTERS
alloy containing in excess of 90% aluminium, the tensile strength could well be higher, 5.65 × 10 ¢ dyne cm - 2 being possible according to the data referenced. Clearly, therefore, the tensile stress of 1.05 × 101° dyne cm - 2 developed by the 5000 A current in each cm length o f the wire will be sufficient to fragment it into a number of small pieces having lengths measured in a few mm. It is submitted that the theory proposed in this paper offers a plausible alternative to Graneau's account of the exploding wire phenomenon. In particular, the stress developed is stronger and is a more direct function of length than applies to the electrodynamic interpretation. Graneau has, by rigorous computer analysis [9] o f microscopic finite current elements, given reason for the existence o f axial stress conditions induced by electrodynamic action between parts o f the same closed circuit. This leaves the question open. However, there is a primary distinction between the two theories which could be exploited in further experimental research. The electrodynamic argument requires induced stress to be proportional to the square of current, whereas the new explanation suggested in this paper involves a linear current relationship. Research into the explosion of wires of different mate-
240
4 February 1985
rials and different cross sections may clarify this issue. Either way, however, the exploding wire phenomenon does draw attention to a new avenue for investigating electrically induced forces as between matter and the field medium. The author acknowledges the kindness of Dr. Graneau in privately demonstrating the exploding wire phenomenon at M.I.T. in September 1982.
References [1] P. Graneau, Phys. Lett. 97A (1983) 253. [2] J. Nasilowski, in: Exploding wires, Vol. 3, eds. W.G. Chace and H.K. Moore (Plenum, New York, 1964) p. 295. [3] P.W. Bridgman, Philos. Mag. 24 (1912) 63. [4] P. Graneau, IEEE Trans. Magn. MAG-20 (1984) 444. [5 ] H. Aspden, Modern aether science (Sabberton, Southampton, 1972) p. 120. [6 ] A.G. Warren, Mathematics applied to electrical engineering (Chapman and Hall, London, 1946) p. 82. [7] W. Ehrenberg, Electric conduction in semiconductors and metals (Clarendon, Oxford, 1958) p. 22. [8] D.E. Gray, American Institute of Physics Handbook, 3rd. Ed. (McGraw-Hill, New York, 1972) p. 2-63. [9] P. Graneau, Nuovo Cimento 78B (1983) 213.
PHYSICS LETTERS
4 February 1985
THE EXPLODING WIRE PHENOMENON H. ASPDEN
Department of Electrical Engineering, University of Southampton, Highfield, Southampton S09 5NH, UK Received 4 October 1984 Revised manuscript received 21 November 1984
Graneau's recent interpretation of the exploding wire phenomenon as an electrodynamic effect verifying Amp6re's classical formulation is questioned. Instead, it is shown that the rupturing force arising from the imbalance of the self-induced electromotive force and the ohmic potential during an explosive current surge will account for the wire breaking into several segments, as is observed.
Graneau [1 ] has recently drawn attention to the phenomenon by which very high currents suddenly applied to a thin conducting wire cause it to explode into several small elements as if subjected to tensile fracture forces which cause the wire to rupture before becoming unduly softened by the ohmic heating. His experiments confirm the earlier findings of Nasilowski [2] by which the wire explosion was permanently arrested to leave wire fragments o f undiminished diameter with fracture faces very nearly perpendicular to the wire axis. Graneau offers a theoretical explanation for this hitherto unexplained phenomenon, basing his argument on the axial forces expected to exist between separate elements of a current circuit according to A m p ~ r e - N e u m a n n electrodynamics as they apply to steady currents. This is in spite o f the rigorous mathematical requirement o f classical electrodynamics that if a current filament is truly circuital the mutual electrodynamic action between an element and the remainder o f the circuit must, on established empirical evidence, involve only forces perpendicular to current flow in that element. Graneau effectively specifies an open circuit condition by which isolated circuit elements are subject to axial forces generated by mutual action o f current in different parts o f the element. The force is o f the form i21og(L/D), where i is the current in absolute amperes and L/D is the ratio of the length o f the element L to a quantity D of the order o f its 238
thickness. With LID equal to 2 000, this gives a tension of 7.6 kg for a current of 10 000 A, which Graneau notes as sufficient for breaking a 1.5 m long copper wire of 1 mm diameter, severely weakened by Joule heating. He justifiably discounts the pinch forces which analysis shows as generating a radial pressure on the surface of the wire corresponding to an axial force of the order o f i2/2. Such forces are too small to cause rupture showing clean tensile fracture. Graneau's emphasis upon the fact that the fractures are tensile in character, whereas pinch forces are compressive and could not cause wire fragmentation of the form observed, can be questioned in the light of experimental research by Bridgman [3]. The application of compressive forces to the cylindrical surface of a rod specimen can cause fracture even though there is no longitudinal stress. Bridgman's surprise at the form of the fracture is clear. He commented "the rupture looks very much like that of a tensile break". More important, however, in challenging Graneau's theoretical account, is the assessment of the magnitude o f the force needed to rupture the wire, particularly as it is not explained why the wire breaks into as many as 50 fragments. Each of these fragments is of insufficient length (far less than 1.5 m) to develop adequate force according to the Graneau method o f calculation. Though in a later paper Graneau [4] discusses the multiple rupturing o f the wire in terms of a progressive weakening o f the residual wire segments with increase 0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 107A, number 5
PHYSICS LETTERS
in temperature, it is felt that an alternative explanation should be sought for this quite remarkable phenomenon. The most obvious cause for an axial force in the path of current flow is the direct action of electromotive force on charge in the conductor. When an emf is applied to a conductor the field intensity E applies force to the electron population having the mobility which accounts for current flow. The forces impart momentum to the electrons which is transferred by collision to the atomic lattice of the conductor. The collision forces are balanced by the action of E upon the positive charge of this atomic lattice. Overall, there is no resultant axial force on the conductor because the emf and the potential drop determined by the collisionrelated ohmic losses are in balance. Thus, in the steady state current condition, the closed circuital flow involves no axial forces along the current path. Now, when the emf is changing owing to magnetic induction effects, including self-induction within the conductor, the applied emf and the potential drop are no longer in balance. Their difference can be measured experimentally and can account for an axial force in the line of current flow [5]. Under these conditions the positive atomic lattice o f the conductor is subject to the full intensity E, as are the electrons, but the electrons have an additional role. They act as a catalyst in transferring momentum to the lattice by collisions, but they also transfer momentum to whatever it is that acts as the store for the energy associated with the magnetic induction process. The field medium is closely coupled with the collective electron action and this field can assert forces in its interaction with charge in matter. In effect, therefore, we can reasonably expect a residual axial reaction force corresponding to the work done by the emf in feeding energy into the selfinductance of the conductor when its current increases. The force will be an axial force acting between the conductor and the field induced in the observer's reference frame by the electron motion. Such a force can cause rupture of the conductor if the current build-up is rapid enough, but it cannot separate the conductor body from the electron population owing to their strong electric coupling. All that can be expected is that the conductor will disintegrate into elements which are contained during the explosion within the plasma formed by the current discharge. The reason for this is that the force acting on each
4 February 1985
positive element of the atomic lattice of the conductor will not, in general, be the same throughout the conductor. The rigidity and internal cohesion of the conductor will determine if it is to withstand the rupturing forces resulting from its inertial reaction with several parts accelerating at different rates. This is the situation (a) if the test conductor is not a perfectly straight specimen so that axial forces in adjacent segments pull in different directions and, more likely, (b) if the current discharge is unstable along its length, as exemplified by the snaking of discharges in high current fusion research, so that, though centred by the conductor chan. nel, some of the flow arcs into surrounding plasma and is not wholly confined to the body of the conductor but asserts forces concentrated on segments spaced along its length. The quantitative analysis fully supports this explanation. The self-inductance of a filamentary conductor is 5 × 10-10 H/cm (see ref. [6]). If a current of the form 10 sin cot amperes flows in this conductor it will develop an emf related to self-inductance and given by 10w cos cot times 5 × 10-10 V/cm. This is an electric field amplitude of 1.67 × 10 - 1 2 t i m e s I 0 w when measured in esu volts per cm. The free electron population in an aluminium conductor is, according to Ehrenberg [7], 2.1 X 1023 per cc and, since electron charge is 4.8 × 10-10 esu, we see that the total atomic lattice charge density balancing the free electron population is about 1014 esu per cc. The action of the electric field on this charge density produces a mechanical force given by 167 (low) dyne c m - 2 per cm length of conductor. In Graneau's experinaent the value o f I 0 was 5 000 A and it was supplied through an inductor by discharging a capacitor bank. The wire exploded as the current oscillated for a few cycles at 2 000 Hz. Thus w was 12 566 and 167 (I0w) then becomes 1.05 X 1010. It follows that our theory requires the aluminium wire used by Graneau in his experiments to be subject to a transient tensile stress of up to 1.05 × 1010 dyne c m - 2 for each cm length of conductor carrying the 5 000 A current. The tensile strength of aluminium depends upon the purity of the material and the manner in which the metal is worked. Reference data [8] quote the tensile strength as 4.74 × 108 dyne cm - 2 for annealed wrought aluminium of high purity and 11.2 × 108 dyne c m - - - f o r the same when cold rolled. However, if the aluminium wire used by Graneau was an 239
Volume 107A, number 5
PHYSICS LETTERS
alloy containing in excess of 90% aluminium, the tensile strength could well be higher, 5.65 × 10 ¢ dyne cm - 2 being possible according to the data referenced. Clearly, therefore, the tensile stress of 1.05 × 101° dyne cm - 2 developed by the 5000 A current in each cm length o f the wire will be sufficient to fragment it into a number of small pieces having lengths measured in a few mm. It is submitted that the theory proposed in this paper offers a plausible alternative to Graneau's account of the exploding wire phenomenon. In particular, the stress developed is stronger and is a more direct function of length than applies to the electrodynamic interpretation. Graneau has, by rigorous computer analysis [9] o f microscopic finite current elements, given reason for the existence o f axial stress conditions induced by electrodynamic action between parts o f the same closed circuit. This leaves the question open. However, there is a primary distinction between the two theories which could be exploited in further experimental research. The electrodynamic argument requires induced stress to be proportional to the square of current, whereas the new explanation suggested in this paper involves a linear current relationship. Research into the explosion of wires of different mate-
240
4 February 1985
rials and different cross sections may clarify this issue. Either way, however, the exploding wire phenomenon does draw attention to a new avenue for investigating electrically induced forces as between matter and the field medium. The author acknowledges the kindness of Dr. Graneau in privately demonstrating the exploding wire phenomenon at M.I.T. in September 1982.
References [1] P. Graneau, Phys. Lett. 97A (1983) 253. [2] J. Nasilowski, in: Exploding wires, Vol. 3, eds. W.G. Chace and H.K. Moore (Plenum, New York, 1964) p. 295. [3] P.W. Bridgman, Philos. Mag. 24 (1912) 63. [4] P. Graneau, IEEE Trans. Magn. MAG-20 (1984) 444. [5 ] H. Aspden, Modern aether science (Sabberton, Southampton, 1972) p. 120. [6 ] A.G. Warren, Mathematics applied to electrical engineering (Chapman and Hall, London, 1946) p. 82. [7] W. Ehrenberg, Electric conduction in semiconductors and metals (Clarendon, Oxford, 1958) p. 22. [8] D.E. Gray, American Institute of Physics Handbook, 3rd. Ed. (McGraw-Hill, New York, 1972) p. 2-63. [9] P. Graneau, Nuovo Cimento 78B (1983) 213.