OTROS

There were four load diameters and two aluminum alloys from which data was collected during the Megagauss IV experiments. The alloys were aluminum 6061, which was the primary load type, and aluminum 1100, which was not used as frequently. The four types of loads were 2mm, 1mm, 0.8mm and 0.5mm diameter aluminum rods.

Because of the sensitivity of our diagnostic, the data collected from the 2mm diameter loads was not discernable from noise levels. Although there is evidence from other diagnostics that the 2mm loads did emit some radiation, the spectrograph/photodiode array could not detect that light. The remaining loads did produce a large enough signal to be distinguished from system noise. The data collected is shown in Table 3.1.

Table 3.1 Collected Data

Shot # Load Type Use of shot 1880 1mm 6061 Early light 1881 1mm 6061 Noise 1883 1mm 1100 All on scale 1885 0.5mm 6061 All on scale 1886 0.5mm 6061 All on scale 1895 0.5mm 6061 All on scale 1896 0.8mm 6061 All on scale 1897 0.8mm 6061 All on scale 1899 0.8mm 6061 All on scale

The early light test was intended to increase signal gain which would in turn increase oscilloscope gain so the signals observed would be representative of the time very close

to when the load began to emit. The noise test was a shot that had the light completely blocked from the detector. This gave us an idea of what sources of noise came from the detector array elements themselves. As it turns out, stray light appears to have contributed very little to the noise levels of the diagnostic. The shots labeled as “All on scale” are examples of data sets where all signals were on the scale set on the oscilloscope, the array was not saturated, and the f# on the camera was set such that the signals would not be cut off by the oscilloscope’s range.

The data collected shows some very interesting results. The early light signals seem to peak in the middle of the visible range, as shown in Figure 3.1.

Figure 3.1 Brightness Spectra at Early Times Shot # 1880

A peak in the visible would seem to correlate well with a blackbody temperature that is around 0.5eV. It is important to note that the signals observed have been timed such that 100ns corresponds to 500kA of Zebra current delivered to the load, or roughly half

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Brightness (AU)

of the peak current. It is also important to point out that brightness is given in arbitrary units because the area from which light was collected is always larger than load radius.

This means that when load radius changes as the thick wire expands, the area of the emitter as seen by the diagnostic is increasing. There was no diagnostic that tracked the radius of the load through every time value collected during the experiment, so determining the area of the emitter is a difficult task. However, it is not necessary to have an absolute measurement of brightness due to emission from the wire because what matters for the understanding of the shape of the spectrum is the brightness amplitudes observed on each array element relative to one another. The area of the emitter is not a quantity that varies with wavelength, so a change in this value will not change the spectrum emitted by the wire. Further still, at each instant in time, the area of the emitter is a constant with regard to the signal observed during that instant, so from element to element, the area of the emitter does not change. Over the short time of observation here, it’s interesting to see that although the peak in brightness is beginning to shift toward the blue end of the spectrum, the element with characteristic wavelength 391.9nm is decreasing in brightness as time goes on. To understand why, we need to look at the data which shows brightness as a function of time for this early time shot. It is shown in Figure 3.2.

Figure 3.2 Brightness Over Time Shot # 1880

We see easily from this plot that element # 21 with characteristic wavelength 391.9nm dips down quite a bit before rising up from zero, and that it does not rise above zero before some of the other element signals are cut off by the range set on the scope. The gain was set higher to observe the early time behavior of the signals, which in the case of element # 21 seems to indicate a drop in current before the rise begins. This current was, of course, not actually negative. We must remember that these signals were shifted down so that the noise level coincided with a brightness level of zero.

If we expected the emitter to remain blackbody throughout its expansion, we would expect that later in time, the spectrum would rise to a peak that is outside the visible range. When we examine the data from the signal producing loads we find that the brightness spectra at later times seem to be rising to a peak outside the visible, but

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Brightness (AU)

that the earlier time still shows a peak in the spectrum at wavelengths in the visible range of the spectrum. Figure 3.3 shows the spectrum of a 1mm load at various times.

Figure 3.3 Brightness Spectra Shot # 1883

It seems that the curve peaks at 450.5nm at early time. We know that if the blackbody spectrum is peaking in the visible range, the temperature must be low. Figure 3.4 shows a blackbody curve peaked at roughly 450nm compared to the spectrum at 137.5ns. In this, and subsequent figures, the scaling amplitude of the blackbody curve was chosen by eye, rather than a least squares fit, owing to the fact that in most cases, visual examination was sufficient to determine whether or not a blackbody spectrum was a good fit. A quick look at Figure 3.4 reveals that the blackbody spectrum is not a very good fit for the experiment data. In addition to the fact that we were expecting a temperature much larger than 0.55eV, the concavity of the two curves is different. As we move forward in time the brightness curves begin to tip up. However, Figure 3.5

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Brightness (AU)

reveals that the blackbody spectrum is still showing some departure from the experimental data at 141.5 ns.

Figure 3.4 Early Time Blackbody Comparison Shot # 1883

Figure 3.5 Mid-Time Blackbody Comparison Shot # 1883 0

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Brightness (AU)

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Brightness (AU)

Wavelength (nm)

Brightness Spectrum

Time 141.5ns Blackbody 2eV

At 149.5ns, the brightness has increased, but the data is no more similar to a blackbody spectrum than the spectrum taken at 141.5ns, as is shown in Figure 3.6.

Figure 3.6 Late Time Blackbody Comparison Shot # 1883

To understand why these times are appropriate we must examine Figure 3.7 which shows how brightness varies, over time. We can see quite easily that some elements rise to a peak at different times, so to avoid confusion with some elements slowing their rate of rise, the time 149.5ns is chosen as the late time because it is far away from any peaks in brightness. It is interesting to note, however, that most peaks seem to occur at roughly the same time as peak current, which happens at roughly 170ns.

We’ve examined the radiation spectrum for the largest diameter from which we were able to collect data, what changes if the diameter decreases? The answer is, not much. Figure 3.8 shows the brightness spectrum for a 0.8mm load.

0

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Brightness (AU)

Wavelength (nm)

Brightness Spectrum

Time 149.5ns Blackbody 2.9eV

Figure 3.7 Brightness Over Time Shot # 1883

Figure 3.8 Brightness Spectra Shot # 1897

The late time spectrum is still rising up to a peak outside the visible, and the earlier time, which compares to 139.5ns from the 1mm wire, is still peaking on the blue end of the

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Brightness (AU)

Wavelength (nm)

0.8mm Diameter 6061 Aluminum Wire Brightness Spectrum

Time 129.7ns Time 139.7ns Time 149.7ns 149.5ns

visible. If we look even earlier it time, the spectrum seems to be almost flat, with a small peak in the blue end of the visible. Figure 3.9 shows the early time data plotted against a blackbody spectrum peaked at 450nm.

Figure 3.9 Early Time Blackbody Comparison Shot # 1897

As with the 1mm diameter aluminum wire, we can see that this peak in the visible range does not correspond well to a blackbody spectrum that is peaked at the same wavelength. The blackbody curve seems to be concave down while the data collected during the experiment appears concave up. Figure 3.10 shows similar results when the spectrum is plotted 10ns later.

0 0.005 0.01 0.015 0.02 0.025 0.03

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Brightness (AU)

Wavelength (nm)

0.8mm Diameter 6061 Aluminum Brightness Spectrum

Time 129.7ns Blackbody 0.55eV

Figure 3.10 Mid-Time Blackbody Comparison Shot # 1897

This time the peaks seem to match quite well but the concavity of the two curves is still different.

Figure 3.11 Late Time Blackbody Comparison Shot # 1897 0

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Brightness (AU)

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Brightness (AU)

The spectrum obtained late in the signal rise, shown in Figure 3.11, appears to conform to a blackbody spectrum, but still shows a disconcerting departure from the blackbody spectrum in the blue. The brightness as a function of time is shown in figure 3.12

Figure 3.12 Brightness Over Time Shot # 1897

We can easily see that there is a second peak in the brightness signal at or around 200ns. This is well after peak current has come and gone, however, the first peak, or what we call the shoulder, does happen before peak Zebra current.

Figure 3.13 shows the brightness spectrum of an expanding 0.5mm diameter load at three times during the rise of signal.

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Figure 3.13 Brightness Spectra Shot # 1895

Now it seems that the latter two times, 109.5ns and 114.5ns, fit better with the blackbody curve, and only the first time, 104.5ns, seems to peak at about 450.5nm.

Figure 3.14 Early Time Blackbody Comparison Shot # 1895 0

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Brightness (AU)

However, we see in Figure 3.14, that this peak does not fit well with a blackbody spectrum peaked at 450nm. The early time plot quite clearly shows that the experimental spectrum is not a blackbody spectrum peaked at 450nm. Later in time, the blackbody fit, shown in Figure 3.15, is quite a bit better, but still shows some departure in the blue.

Figure 3.15 Late Time Blackbody Comparison Shot # 1895

The radiation signals from the photodiode array are shown as functions of time in Figure 3.16. We notice that the fast rise of the radiation emitted from the wire seems to happen about 30ns sooner with the 0.5mm diameter wire than with the 0.8mm diameter wire. Almost immediately after 500kA is reached, the wire begins to light up.

0

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Brightness (AU)

Figure 3.16 Brightness Over Time Shot # 1895

It is clear that, although this small wire begins to emit light faster than the 1mm or 0.8mm diameter wires, we again see that the second peak occurs well after peak load current. The complicated behavior of the load at times after peak current, which in all cases shows instabilities in the wire, is not something we have labored to understand at this time.

Conclusion

We set out to determine whether the visible radiation emitted from a thick wire pulsed with multi-megagauss fields is from a blackbody source. Through analysis of the experimental evidence collected by the diagnostic described in Chapter 1, we find that the visible light spectrum is not simply described as a blackbody spectrum. It appears that at early time the brightness peaks in the visible part of the spectrum, which would correspond to a temperature of less than 1eV if the wire were emitting like a blackbody.

However, this is not a conclusion supported by the evidence gathered by other diagnostics in this experiment⁵, nor by comparison of the data to blackbody spectrum.

As time progresses, it looks as though the spectra still support the idea of a blackbody emitter except in the blue end of the spectrum, where the spectra seem to fall short of the expected shape of the brightness associated with blackbody. There could be several reasons for this, but the analysis to date does not lend itself to any strong conclusions. It could be that in later time, the peak of the blackbody curve is simply at a wavelength that is just outside the visible range, so that the curve appears to fall short of a higher temperature blackbody curve because it is rounding off toward a peak. However, the brightness temperature with detectors that have an absolute calibration⁵ suggest temperatures too high for this to be possible. In addition, the full formula blackbody spectrum plotted at a temperature which would correspond to a peak in wavelength that is just outside the visible range still shows a departure from the blackbody in the blue.

With this in mind, we conclude that the spectra we observed from the exploding wire depart in some way from the simple blackbody assumption. Comparing the brightness signals to the current waveform directly or accounting for the fact that the area of the emitter is not constant in time, may reveal more conclusive evidence supporting the notion that the wire is emitting radiation with blackbody spectra. It will also be important to add the transmission factors from the vacuum window and the microscope slide to the calibration of the emitted radiation signals. Doing so may reveal a better agreement with blackbody spectra.

It is also reasonable to postulate that the radiation emitted from the thick wire as it explodes is not completely blackbody. Preliminary estimates by numerical modeling suggest that the observed spectrum can be explained by taking into account the finite optical thickness of the plasma layer combined with the fact that the temperature varies throughout the layer. In any case, further analysis is required to gain a more complete understanding of the observed radiation spectra emitted from the exploding wires.

References

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2F.F. Chen (1984), Introduction to Plasma Physics and Controlled Fusion, Volume 1: Plasma Physics, 2^nd Edition, Springer-Verlag, New York.

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6 A. Grinenko (2006). Nanosecond time scale, high power electrical wire explosion in water.

Physics of Plasmas .

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8E.A. Martin (1960). Experimental Investigation of a High-Energy Density, High-Pressure Arc Plasma. Journal of Applied Physics, Volume 31, pp. 255-267.

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12A.Einstein (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt". Annalen der Physik Volume 17, pp.132–148.