SMALL HELICAL MAGNETIC FLUX COMPRESSION GENERATORS: EXPERIMENTS AND ANALYSIS∗

P. Appelgrenξ, G. Bjarnholt, M. Elfsberg, T. Hurtig, A. Larsson† and S. E. Nyholm Swedish Defence Research Agency, FOI

Defence & Security, Systems and Technology, SE-147 25 Tumba, Sweden

∗ Work supported by the Swedish Armed Forces ξ email: patrik.appelgren@foi.se, Academic affiliation: Space- and Plasma Physics, School of Electrical Engineering, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden † also with the Division for Electricity, Uppsala University, Sweden

Abstract This paper presents experimental results with helical magnetic flux-compression generators (FCGs). FCGs convert the chemical energy bond in explosives into electric energy. The generator had an initial inductance of 23 µH and was operated into a load of 0.2 µH. The generator is charged with 0.27 kg of high-explosives (PBXN-5). Various types of diagnostics were used to monitor the operation of the generator, including current probes, optical fibres, and piezo gauges. The results are analysed and the expansion of the armature compared with hydrodynamic simulations.

I. INTRODUCTION Small helical magnetic flux compression generators (FCGs) are attractive energy sources for compact pulsed power systems [1, 2]. Of special interest is to use an FCG together with a pulse forming network, PFN, to provide a high voltage pulse to drive microwave generators to generate high-power microwaves (HPM), [3]. This paper presents briefly the design of, results from and analysis of experiments with two generators, FCG #1 and FCG #2. Different types of diagnostics were used and by combining and comparing data from different diagnostics it is possible to analyse various properties of the generator and events during operation. It was decided that the generators were to be seeded with different currents, where the first generator (FCG #1) was to be seeded with modest current, while the second (FCG #2) was to be seeded with more current than it was designed for. Hence, in the first experiment the current amplification could be expected to be higher than in the second where higher resistive losses could be expected. The generators were operated short circuited by a return conductor and the loading consists only of that part and the generators final inductance. The results are used in the development of simulation models for FCGs [4].

II. DESCRIPTION OF THE FOI FCG

The FCG has been described elsewhere [5, 6] and only a brief presentation is given here. The FCG has a length of 300 mm and a diameter of 70 mm. The initial inductance is 23 µH and the final inductance is 0.2 µH. The stator, Fig. 1, is comprised of a helical coil machined from a copper tube, and has four sections. The pitch and conductor width of each section are given in Table 1. The coil conductor has a rectangular cross section with a thickness of 1.5 mm. The last section has a slightly larger inner diameter of 55 mm. In connection to the machining of the coil, epoxy was applied as insulation between the turns. A 0.25 mm layer of epoxy was applied to the inner surface of the coil to increase the electrical breakdown strength.

240330

2024 47.5

44.58.0°

53

Section 2Section 1 Section 3 Section 4

289

55

Figure 1. The dimensions of the FCG stator (above) and armature (below).

Table 1. Stator properties. Section Number

of turns Pitch [mm]

Section length [mm]

Conductor width mm]

1 24 3.5 84 2 2 11 5 55 3 3 8 6 48 4 4 7 7 50 5

The epoxy layer of the last section is thicker, 1.25 mm,

to prevent electric breakdown during the final compression at which a high internal voltage is developed. The high-explosives loaded copper armature consists of a cylindrical part and a conical part machined from one single piece of copper, see Fig. 1. The outer

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diameter of the cylinder is 24 mm and the inner diameter is 20 mm. The conical end coincides with the last section (section 4) of the stator and has a cone angle of 8°. The high explosive is point initiated to detonation at the cylindrical end of the armature (left in Fig. 1) using a precision initiator. When the detonation front moves into the armature it will be accelerated outwards and will form a cone moving forward shorting out the turns. When this expanding cone (A) meets with the conical end (C) of the armature they are designed to form a more or less cylindrical part moving radially outwards towards the stator (D), as illustrated by hydrodynamic simulations using GRALE [7] in Fig. 2. The pressure inside the explosive is shown which is highest at the detonation wave front (B). The reduction in inductance becomes very rapid and thus the increase in current.

1 2

3 4

B A C

D

Figure 2. Hydrodynamic simulations of the armature movement in section 4 as the detonation wave front (B; indicating the pressure) progress to the right. The time between the frames is 4 µs.

The expanding armature will make initial contact with the stator via a copper ring (crowbar ring) mounted on the stator. The two generators have different crowbar rings. Based on the experience of the first experiment with FCG #1, the crowbar was modified for FCG #2, resulting in a shorter crowbar with a sharper edge and a glide plane angle of 31°. The change served to minimise ejection of copper which could cause problems inside the FCG. The explosive used in the generator is three pieces (0.27 kg) of plastic-bonded high-explosive PBXN-5 (95% HMX / 5% Viton A), machined to fit into the armature. The armature was heated and the explosive cooled in order to press fit the explosive into the tube. The PBXN-5 detonation velocity is 8.8 km/s and its mass density is 1840 kg/m3. The high explosive was point initiated with a precision initiator to avoid asymmetries in the detonation process.

III. DIAGNOSTICS

To monitor the generator operation different diagnostics were used. To monitor the current, a differential Rogowski coil was built and mounted around the return conductor of the generator, I in Fig. 3. A Pearson 1423 probe was used to monitor the seed current. Thus, the Rogowski coil could be calibrated to the common current up to the time of crowbar. Optical fibres were mounted at various positions on the generator and in the initiation chain, see Fig. 3. They were used to monitor the times

when the detonation front reached different positions in the high-explosive and to monitor events related to the collision of the armature and stator and the contact point behaviour. Piezoelectric shock sensitive contact pins were mounted on the stator to determine space-time characteristics of the armature/stator impact. The piezo gauges drives a light emitting diode mounted on an optical fibre to provide electric insulation between the FCG and the diagnostics. Table 2 shows the type, position and purpose of the diagnostics used in FCG #1 and #2. All diagnostics were triggered on the rising flank of the current pulse initiating the detonator via a signal obtained from a pick-up coil, providing a common time reference.

71110

188149

215

240265

A EDB C FI

HG

J,KL

Figure 3. The position of the diagnostics used in the experiments. A to L indicates the positions of various diagnostics, see Table 2.

Table 2. Diagnostics in the two generators Diagnostic Position Purpose Optical fibre FCG #1 and #2

A Timing of the detonation wave front in det. cord

Optical fibre FCG #1

B,C,D,E Monitor the passage of the contact point

Piezo gauge FCG #1

B,C,D,E,

Monitor the impact of the armature with stator

Piezo gauge FCG #2

F,G,H Monitor the impact of the armature with stator

Current probe FCG #1 and #2

I Monitor the current

Optical fibre FCG #1

J Monitor the light inside FCG, one fibre

Optical fibre FCG #2

K Monitor the light inside FCG, 3 fibres 120° apart

Optical fibre FCG #1 and #2

L Timing of the detonation wave front in explosive

IV. RESULT AND ANALYSIS

The experiments were performed outdoors and the generators were placed inside a steel cylinder with a wood support to absorb shrapnel from the generator. A 67 µF capacitor bank was used to seed the flux compression generator via four RG213 cables. The generator was crowbared just before the peak of the seed current occurring at around 60 µs. Both experiments were successful with good recordings from the all the probes.

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In this section various results are presented and analysed in order to understand the generator performance.

A. Current characteristics Figure 4 shows generator currents for FCG #1 and FCG #2. At crowbar time the seed currents were 5.7 kA and 11.2 kA respectively and the peak currents were 269 kA and 436 kA. Thus the current amplification factor is 47 for FCG #1 and 39 for FCG #2. The lower current amplification of FCG #2 is thought to be due to resistive losses in the generator during the final compression. The difference in operation time (30.1 µs for FCG #1 and 31.4 µs for FCG #2) is due to the modified crowbar ring in FCG #2. The double-arrows indicate the approximate time interval during which the contact point is within a specific section.

60 65 70 75 80 85 900

100

200

300

400

500

Time (µs)

Cur

rent

(kA

)

b)

FCG #1269 kA: 86.6 µs

FCG #2436 kA: 87.6 µs

Section 1 Section 2 Section 3

Figure 4. The FCG current recordings in experiments with FCG #1 and FCG #2. The double-arrows indicate the approximate time interval during which the contact point is within a specific section.

60 65 70 75 80 85 90

10−1

100

101

102

Time (µs)

Cur

rent

tim

e de

rivat

ive

(GA

/s)

Section 1 Section 2 Section 3

FCG #1

76 78 80 820

5

10

15

20

Time (µs)

Cur

rent

tim

e de

rivat

ive

(GA

/s)

Section 2: Pitch 5 mm;Oscillation period 5/8.7 µs = 0.57 µs

Section 3: Pitch 6 mm;Oscillation period6/8.7 µs = 0.69 µs

Section 2 Section 3

FCG #1

Figure 5. Current time derivative of FCG #1 (a). Minor 2π-clocking in FCG #1 with oscillation period close to the ratio of section pitch to detonation velocity (b).

The current time derivative for one of the generators, FCG #1, is plotted in Fig. 5a. The maximum current time derivatives are 1.35⋅1011 A/s and 1.8⋅1011 A/s for the two generators respectively. The current time derivative reveals the presence of 2π-clocking, a phenomena caused by coaxial misalignment of the armature and the stator. This is observed as oscillations with a period close to the ratio of the pitch to the detonation velocity. Minor 2π-clocking could be observed in FCG #1, Fig. 5b.

B. Detonation velocity The detonation velocity of the explosive is obtained from the optical fibres signals (position A and L in Fig. 3). Dividing the length of the explosive by the time difference between the signals compensated for the time delay in the detonator and precision initiator gives the detonation velocity. Detonation velocities of 8.70 km/s and 8.64 km/s are obtained in good agreement with the data for the explosive PBXN-5 having a detonation velocity of 8.8 km/s.

C. Axial contact point velocity The optical fibres and piezo gauges mounted on the stator (position B, C, D and E in Fig. 3) can be used to obtain a value of the axial velocity of the contact point. An axial contact point velocity of 8.59 km/s is obtained for the optical fibres and 8.54 km/s for the piezo gauge. This is slightly lower than the measured detonation velocity which at steady state should be identical to the contact point velocity.

D. Light emission inside generators The optical fibres used to monitor the light inside the generator were mounted at the generator end (position J and K in Fig. 3). In both generators small oscillations in the optical signals are visible and originate from the rotating contact point. The period of the oscillations relates to the pitch and can be used to obtain a value of the axial contact point velocity. The values obtained, Table 3, agree with the detonation velocity measured in the explosive but is slightly higher than that obtained from the piezo gauges and optical fibres mounted along the stator.

Table 3. Axial contact point velocities obtained from

intensity variations in the light observed by optical fibres. FCG #1

section2 FCG #1 section3

FCG #2 section1

FCG #2 section2

velocity [km/s]

8.64 8.76 8.71 8.80 8.67

8.70 8.72 8.71

E. Deflection angle of the armature Since the position of the detonation wave front and the contact point along the stator is known it is easy to estimate the deflection angle (Gurney angle) of the

b)

a)

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armature at time of crowbar and when the expanded cone is in contact with the stator and passes one of the optical fibres. From the point initiated boost charge (PBXN-5) a spherical propagation of the detonation wave front at 8.7 km/s is used as obtained in experiments. Assuming that the inert shock from the detonation front in the copper armature lags the detonation front by 2 mm at the outer surface of the armature, the generator CAD-drawing can be used to find the deflection angle. The 2 mm lag was observed in hydrodynamic simulations using a FOI code GRALE [7] of the armature expansion of this specific armature. A straight line originating from the outer armature surface (at A in Fig. 6) is drawn to be a tangent to the crowbar ring (at B) and the angle is measured to be 8.4°. An angle of 8.6° was obtained in the GRALE simulation.

8.4°

R91.4

AB

Figure 6. Estimation of the deflection angle of the expanding armature at crowbar (top) and the corresponding hydrodynamic simulation (bottom).

A similar estimate can be obtained for FCG #2 and the

angle is then found to be 7.7° with simulated value of 7.8°. The inner edge of the crowbar ring of FCG #2 is closer to the armature and the armature has not had the time to accelerate, explaining the smaller angle.

9.6°

R241

Figure 7. Estimation of deflection angle of the expanding armature (top) and the hydrodynamic simulation (bottom).

The deflection angle of the armature when in contact with the stator is determined in a similar way as for the angle at crowbar. With the assumed 2 mm lag of the armature expansion a line is drawn to the position of the optical fibre, Fig. 7. Using the drawing the deflection angle is determined to 9.6°, which is in good agreement with the 10.1° obtained in GRALE simulations.

V. CONCLUSIONS

Two FCGs were prepared with different diagnostics to monitor the FCG operation and were successfully tested. The higher seed current amplitude in the second generator degraded the performance possibly due to excessive heating of the stator and armature causing resistive losses. The generators showed small (FCG #1) or no 2π-clocking (FCG #2) indicating good alignment of the armature with the stator and a good point initiation of the high explosive. Based on recordings from diagnostics viewing into the generator, mounted on the stator or in the high explosive, values of the detonation and axial contact point velocities were obtained and were found to be in good agreement with expected values. The deflection angle of the armature could be estimated by combining the data from different diagnostics and are compared to hydrodynamic simulations.

VI. REFERENCES

[1] L. L. Altgilbers et al. “Magnetocumulative

Generators”,Springer-Verlag, New York (2000). [2] A. A. Neuber (ed). “Explosively Driven Pulsed

Power”, Springer-Verlag, Berlin Heidelberg. (2005). [3] B. M. Novac et al, “10 GW Pulsed Power Supply for

HPM Sources”, Transactions on Plasma Science, Vol. 34, Oct. 2006, pp 1814 - 1821

[4] P. Appelgren et al, “Modelling of a small helical magnetic flux compression generator”, to be published in Proceedings of IEEE Pulsed Power and Plasma Science Conference, Albuquerque, USA, 2007

[5] P. Appelgren et al, “Design of and experiments with small helical magnetic flux compression generators”, to be published in Proceedings of Megagauss XI, London, UK, (2006)

[6] P. Appelgren et al, “Analysis of experiments with small helical magnetic flux compression generators”, to be published in Proceedings Megagauss XI, London, UK, (2006)

[7] L. Olofsson, and A. Helte, “GRALE2D – an explicit finite element code for two-dimensional plane and axi-symmetric multi-material ALE simulations,” Computational Ballistics II, Southampton: WIT Press, pp. 137-145, (2005).

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