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Optical investigation and numerical simulation of prebreakdown in a hollow cathode pseudospark discharge
Nuclear Instruments and Methods in Physics Research A294 (1990) 411-416 North-Holland
OPTICAL INVESTIGATION AND NUMERICAL SIMULATION OF PREB EA IN A HOLLOW CATHODE PSEUDOSPARK DISCHARGE
OWN
Christoph SCHULTHEISS, Karl MITTAG *, Daniele DIETRICH and Walter BAUER
Kernforschungszentrum Karlsruhe GmbH. Institut für Neutronenphysik und Reaktortechnik, Postfach 5640, H-7500 Karlsruhe, FRG Received 12 April 1990
The ionization growth during the prebreakdown phase of the pseudospark discharge is simulated within the hollow cathode region using a fluid model . Stimulated by the results of these simulations, an experimental investigation in an identical geometry was carried out, measuring the light emission during the prebreakdown phase . The numerical results for the discharge current and the tight emission agree qualitatively with the experimental ones .
1. Introduction The pseudospark is a fast pulsed discharge at low gas pressure and high voltage in a special hollow cathode geometry [1-3]. Its physics can be studied best in a simple diode device (fig. 1), consisting of anode and cathode separated by an insulator. Its most essential feature is a hole in the center of the cathode giving access to a hollow cathode region outside the anodecathode gap . More sophisticated arrangements are used for high-voltage applications [3-6], such as fast switches or the generation of self-pinched electron beams, X-rays and ions. From various experiments it is well known that most important for the occurrence of a pseudospark is the discharge physics in the hollow cathode during the prebreakdown phase, which lasts of the order of microseconds. This phase ends with an extremely fast current rise correlated with a fast breakdown in voltage during a time interval of 10 to 100 ns. In order to obtain a better understanding of the hollow cathode processes, numerical simulations based on a fluid model have been carried out [7] . It was shown that as a result of the special hollow cathode geometry, a space charge triggered positive feedback mechanism causes an overexponential growth in charge densities on the axis in the region or the note. his is responsible for the very fast onset of the breakdown . Stimulated by the results of the simulations, the It t emission from the hollow cathode of a pseudospark diode was measured by means of time- and space-re-
solved optical spectroscopy . This paper compares the results of this experimental work with the corresponding results from the numerical simulation .
Experiments with a slightly different hollow cathode geometry using streak camera photography have shown that indeed the discharge starts from a point on axis near the hole [8] .
2 . Experimental
investigation
The aim of the experiments was to measure the time the nitrogen line emission in the prebreakdown phase of a pseudospark . For intensity reasons, this measurement is strongly restricted by the limited sensitivity of the de-
development of the radial distribution of
tectors, namely diode arrays.
Anode
'r
" Kernforschungszentrum Karlsruhe Datenverarbeitung in der Technik .
GmbH,
Institut
für
.Grid Fig . 1 . One-gap pseudospark chamber, which is used in the optical observations and in the numerical simulations . The upper part is the anode separated from the hollow cathode by an insulator . In addition, the position of the Langmuir-probe in the hollow cathode is shown . The optical path is drawn in radially enlarged at the ams .
0168-9002/90/$03 .50 (0 1990 - Elsevier Science Publishers B .V . (North-Holland)
412
C. Schuitheiss et al. / Investigation andsimulation ofprebreakdown
Fig. 2. Total current of the pseudospark discharge (t = 0 when the voltage drops to i of its maximum value) . Two lines were investigated which are excited with sufficient strength in the discharge. The strongest is the 391 .4 nm N2 II-ion line; the second one is the 632.2 rum excitation of N2 I. Both lines are band heads of the First Negative System which appears typically in lowpressure discharges. The intensity of the neutral line is about 20 times lower than that of the strongest ion line. Fig. 1 shows the chamber which consists of ~n anode/cathode gap and a hollow cathode region . The depth of the hollow cathode as well as the anode cathode gap is 10 mm; the diameter of the axial bore hole is 5 mm and the disc thickness is 4 mm. In addition the position of a floating Langmuir probe is shown,
Fig. 3. Current detected by the floating Langmuir probe with an active area of 50 mm2 (time-scale : see fig. 2).
Fig. 4. Time development of the intensity of the 391 .4 nm nitrogen line measured on the axis (time-scale : see fig. 2) .
C. Schultheiss et al. / Inwstigation and simulation ofprebreakdown
which was used to give an early trigger signal to the optical spectral multichannel analyser (OSMA, spectral resolution : 1 .59 nm/mm, focus length 0.5 m, time resolution 12 ns). Furthermore, fig . 1 shows the light cone accepted by the optical system. Within a solid angle of 1 .02 x 10-° sr light passes a quartz window at the bottom of the hollow cathode, crosses the optical system and reaches the diode array at the exit of the spectrometer. The optical system has a focus diameter of 100 pm; the cone opens at the quartz exit to 285 pm. To vary the radial position of the optical path, the chamber itself can be shifted radially by means of a micrometer system . The step width is 0.2 mm. Since the optical paths overlap between the step widths, an unfolding procedure was necessary afterwards. The pseudospark chamber was connected with a 1 nF capacitor and charged via a resistance to 6 kV. In the self-breakdown mode at a pressure of 10 Pa the measurements were carried out with a repetition frequency of about 20 Hz. Fig. 2 shows the total discharge current as a function of time. For the experimental analysis the time zeropoint is defined as the time, at which the applied voltage has dropped to 1' . Fig . 3 gives a logarithmic plot of the current detected by the floating Langmuir probe also as a function of time. Here a feature typical for the pseudospark can be observed : The probe current has a positive polarity from the very beginning. In LTE
105 El
N c ar c
413
Radius
( cm I
Fig. 6. Intensity of the 632 .2 rim nitrogen I line as a function of radius and time (time-scale: see fig . 2).
plasmas the polarity normally is negative . Further, the usual zero balancing of the probe current by means of an applied bias voltage is not possible for times later than -200 ns. Obviously the Langmui: theory of a floating probe fails in our case. This may be explained by the fact that in addition to a flow and counterflow of electrons and ions to the probe it is also irradiated by photons with an energy in the order of 100 eV . This VUV radiation causes a loss of electrons due to the photo effect which is responsible for the positive charge of the probe. Fig . 4 shows as an example the time development of the 391 .4 rim line of nitrogen ions in the region between -100 ns and + 150 ns directly on the axis. Because of a too low light intensity, it was not possible to obtain spectra in the time region before -100 ns although up to 20 single measurements were added . The same can be stated for the 632 .2 rim line, for which the earliest signal could be measured 60 ns ahead of the time zero-point . Figs. 5 and 6 summarize the analysis (id ih e ni sured photon flux density for different radii and times of the two nitrogen lines. All intensity plots show a peak between the axis and r = 0.2 mm, which means with a that in this integration interval a central b radius r < 0.2 mm is embedded. A systematic dip of the measured point at r = 0.2 mrn results from the unfolding procedure mentioned above. n
10 1 '
e
0.0
e
.
I . 0.1
t
s
I . . . A . 0.2 0.3
t
-
I
e
0.4
-
i I . i I 0.5 0.6
Radius
e
[cm l
e
t
0.7
Fig. 5. Intensity of the 391 .4 rim nitrogen II line as a function of radius and time (time scale: see fig. 2).
_a
C: Schultheiss et al. / Investigation and simulation ofprebreakdown
414
3. Numerical simulation of the prebreakdown in a hollow cathode geometry 3.1. Simulation parameters The simulations were performed for the geometry shown in fig. 1. The voltage taken was 6 kV, constant in time, which equals the peak voltage in the experiments described above . In order to observe an ionization growth in the simulations the pressure had to be chosen larger than in the experiments, namely 130 Pa. In addition, a high photon secondary coefficient of 0.4 was required to produce enough secondary electrons to yield a growth in densities. From the discrepancy with respect to the onset of ionization growth between experiments and simulation, it follows that some major causes for charge carrier muiiipiication are missing in the model. The reason is that all discharge physics in the hole and gap regions are neglected. Therefore, the effect of slow and fast ions, or fast neutrals hitting the disc in the hole region releasing secondary electrons there, as well as the secondary electrons from the light produced in the gap between anode and cathode are missing. Also, fast ions (or neutrals after charge exchange) having gained energy in the keV range in the anode-cathode gap, passing through the HCR fast, then hitting the wall opposite the hole may release a significant fraction of secondary electrons . For example, it was shown, that such a fast ion flux with a current density of only 1/100 of that of the electrons leaving the hole was equivalent to reducing the required photon secondary coefficient by a factor of 20. 3.2. Results of the simulations
influence is still negligible . The initial low level electron density is assumed to be uniform in space, and the ion density is taken to be zero. The total electron current leaving the HCR is shown as a function of time in fig. 7. The electron current density at the hollow boundary across the hole is shown in fig. 8, with the time as parameter. At time zero the
N z= U c-+
v
x
In the theoretical analysis the time zero is defined at the begin of the simulation at which the space charge --3 .
z 0 0 v J
v
z w
Fig. 8. Electron current density at the hollow cathode boundary across the hole with time as parameter (time-scale : see fig. 7).
-q .
I
:5 -5 .
0
LL.11_:-LU1~
200
q00
L~
1 ' ' . ._L ' . ' ' '
600
800 1000 TIME (N5)
Fig. 7. Total electron current leaving the hole as function of time (t = 0 at the start of the simulation) .
Fig. 9. Photon flux density at the end wall in the hollow cathode region as a function of radius with time as parameter, integrated over an 0.2 mm optical channel perpendicular to the end wall (time-scale : see fig. 7).
C. Schuitheiss et al. / Investigation and simulation oferebreakdown
initial electrons start to move, producing secondary electrons and ions by impact ionization in the volume. Exitation and photon emission causes secondary electrons at the walls in the HCR. After about 20 ns the initial electrons have left the HCR through the hole, and a self-consistent solution of the equations remains . This effect is seen in figs. 7 and 8 initially. Next follows a period in time during which the growth in current and densities is exponential. During a transition phase, the growth rate gets gradually overexpontial across all of the hole. During this phase, the positive ion space charge inside the HCR starts to change the electric field . Finally, during a very short time of only several ns, the growth in current density in the vicinity of the axis explodes, and a high current density, small diameter electron beam leaves the HCR . At this time the total electron current leaving the hole is of the order of a mA. The photon flux density at the end wall in the HCR is shown in fig. 9 as a function of radius with time as parameter . In order to be comparable to the experiments reported above, the light originating inside the HCR in a cylinder of 0.2 mm diameter, perpendicular to the end wall, was integrated. 4. Matching of the simulation- and experimental time scale To compare the experimental results with those of the numerical simulation, one has to keep in mind that the simulation starts at a time for which the space charge influence is negligible, and ends at the onset of the current instability, whereas the spectroscopical experiment starts at the first observable light emission and ends at the beginning of the main discharge . The relation between the different time scales can be found by an estimation of the observed photon flux density. Assuming a spectrometer opening time of 12 ns, a number of 500 photons as statistical observation limit, 4 channels as detector resolution, about 10 lines over which was integrated and putting in the actual geometrical properties a photon flux density of 6 x 102° (scm2)-1 is estimated as the observation limit. This is more than 1018 (s cm2 )-1 ; the value reached in the simulation . From this argument we have to conclude, that the measurements start at some time aiier thc simulation had already ended. The simulation ends at 962 ns; from fig . 9 one concludes, that on the average the light emission in the hollow cathode approximately increases by a factor of 10 every 20 ns. Extrapolating, the photon flux density in the hollow cathode would reach the experimental threshold value of 6 x 102° about 100 ns later, which means at a simulation time 1060 ns. thus the time difference between the end of the simulation and the time zero of the experiment (see figs. 4 and
41 5
Time t ns I Fig. 10. Overview on the measurements and a comparison with the total current of the simulation on the common time scale determined . A time gap of about 100 ns separates the end of the simulation and the beginning of the visible light detection. The VUV detection (Langmuir probe) extends into both time scales and shows a transition behaviour just at the time where the simulation ends. The total current of the simulation is scaled to match the VUV curve in one point. 5) is about 200 ns. This can be confirmed by extrapolating the experimentally observed total current (fig. 2) back to a level of 1 mA at which the simulation was stopped (see fig . 7). Fig. 10 shows a summary of the measurements and the total current of the simulation on the common time scale just determined . The logarithmic ordinate is in arbitrary units. Since the average light emission is proportional to the average current of the simulation the current is adapted to the VUV radiation curve by applying a scale factor. In the next section fig. 10 will be discussed in detail . 5. Comparison of simulation and ex
riment
of the wh-n nsav densities 1!t ..~.... .., 51 14V111PW1JV11 VA L114 tliel3EVS6 ®eas e densities a.. fig's
6 and 9 shows that simulation and experiment agree qualitatively. The sharp maximum of the light intensity on the axis and its radial decrease into the hollow cathode area are similar in the experiment and in the simulation . This is an important result because the simulation predicted that the onset of the pseudospark happens on the axis close to the hole, and this is in accordance with our experimental results . This measurement also agrees with side-on streak measurements for a
416
C. Schultheiss et al. / Investigation andsimulation ofprebreakdown
one-gap pseudospark chamber [8] where the first light emission was observed in a small area on the axis at the exit of the hollow cathode. From fig. 10 it can be seen that except for the Langmuir probe measurement no time overlap between experimental measurements and simulation exists and therefore the theoretically predicted overexponential rise of the visible photon flux could not be observed experimentally in principle. The time development of the total current in the simulation during the overexponential rise and the increase of exponential growth of the early signal of the Langmuir probe can be interpreted as a change of the discharge properties : The onset of VUV radiation indicates that an increasing amount of electrons become run-away and start to generate bremsstrahlung and K-radiation in the working gas. This means that the fluid model of the simulation starts to fail since the movement of the electrons is no longer determined by the local electric fields only . After this change of discharge properties, both the VUV and the visible light intensity grow exponentially again . For this discharge phase another physical model is required [9]. In addition, it must be recalled that there is a difference in the pressure. :f the experiments are operated at the pressure used in the simulation (p =130 Pa), no pseudospark would appear. On the other hand, with the experimental pressure (p = 10 Pa) the simulation shows an exponential decay of the initial charge densities rather than a buildup of the discharge. This is not surprising, since in the real experiment a number of effects contribute to the production of charge carriers which are not included in the model, e.g. enhanced emission from surfaces due to adsorbates, as well as light, fast neutrals and ions coming from the main gap into the hollow cathode.
With these restrictions in mind it is fair to state that the experiments support the results of the simulations.
Acknowledgements Stimulating discussions with A. Citron, A.J. Davies, W. Hartmann, W. Niessen, P. Choi and W. Schmidt were valuable and encouraging for this work.
References [11 J. Christiansen and Chr. Schultheiss, Z. Phys. A290 (1979) 35 .
[21 W. Bauer, A. Brandelik, A. Citron, H. Ehrler, E. Halter, G. Melchior, K. Mittag, A. Roper and Chr. Schultheiss, Laser and Particle Beams 5, part 4 (1987) 581. [31 W. Bauer, H. Ehrler, F. Hoffmann, K. Mittag and N. Niessen, Proc. 7th Int. Conf. on High Power Particle Beams, Karlsruhe (1988) p. 233. [4j J. Christiansen, in: The Physics and Applications of High Power Hollow Electrode Glow Switches, ad. M.A. Gundersen (Plenum, New York, 1990) to be published. [5J K. Frank, J. Christiansen, O. Almen, E. Boggasch, A. Görtler, W. Hartmann, C. Kozlik, A. Tinschmann and G.F. Kirkman, in Proc. Int. Society for Optical Engineering, Innovative Science and Technology Symp. (Los Angeles, 1988) 173. [61 P. Billaut, H. Riege, M. van Gulik, E. Boggasch, K. Frank and R. Seeb6ck, CERN-rep. 87 (1987) 13 . [7] K. Mittag, P. Choi and Y. Kaufman, Nucl. Instr. and Meth. A292 (1990) 465. [8] P. Choi, H. Chuaqui, J. Lunney, R. Reichle, A.J. Davies and K. Mittag, IEEE Trans. Plasma Sci. 17 (1989) 770. [9] A.B. Parker and P.C. Johnson, Proc. R. Soc. Lond. A325 (1971) p. 512.
OPTICAL INVESTIGATION AND NUMERICAL SIMULATION OF PREB EA IN A HOLLOW CATHODE PSEUDOSPARK DISCHARGE
OWN
Christoph SCHULTHEISS, Karl MITTAG *, Daniele DIETRICH and Walter BAUER
Kernforschungszentrum Karlsruhe GmbH. Institut für Neutronenphysik und Reaktortechnik, Postfach 5640, H-7500 Karlsruhe, FRG Received 12 April 1990
The ionization growth during the prebreakdown phase of the pseudospark discharge is simulated within the hollow cathode region using a fluid model . Stimulated by the results of these simulations, an experimental investigation in an identical geometry was carried out, measuring the light emission during the prebreakdown phase . The numerical results for the discharge current and the tight emission agree qualitatively with the experimental ones .
1. Introduction The pseudospark is a fast pulsed discharge at low gas pressure and high voltage in a special hollow cathode geometry [1-3]. Its physics can be studied best in a simple diode device (fig. 1), consisting of anode and cathode separated by an insulator. Its most essential feature is a hole in the center of the cathode giving access to a hollow cathode region outside the anodecathode gap . More sophisticated arrangements are used for high-voltage applications [3-6], such as fast switches or the generation of self-pinched electron beams, X-rays and ions. From various experiments it is well known that most important for the occurrence of a pseudospark is the discharge physics in the hollow cathode during the prebreakdown phase, which lasts of the order of microseconds. This phase ends with an extremely fast current rise correlated with a fast breakdown in voltage during a time interval of 10 to 100 ns. In order to obtain a better understanding of the hollow cathode processes, numerical simulations based on a fluid model have been carried out [7] . It was shown that as a result of the special hollow cathode geometry, a space charge triggered positive feedback mechanism causes an overexponential growth in charge densities on the axis in the region or the note. his is responsible for the very fast onset of the breakdown . Stimulated by the results of the simulations, the It t emission from the hollow cathode of a pseudospark diode was measured by means of time- and space-re-
solved optical spectroscopy . This paper compares the results of this experimental work with the corresponding results from the numerical simulation .
Experiments with a slightly different hollow cathode geometry using streak camera photography have shown that indeed the discharge starts from a point on axis near the hole [8] .
2 . Experimental
investigation
The aim of the experiments was to measure the time the nitrogen line emission in the prebreakdown phase of a pseudospark . For intensity reasons, this measurement is strongly restricted by the limited sensitivity of the de-
development of the radial distribution of
tectors, namely diode arrays.
Anode
'r
" Kernforschungszentrum Karlsruhe Datenverarbeitung in der Technik .
GmbH,
Institut
für
.Grid Fig . 1 . One-gap pseudospark chamber, which is used in the optical observations and in the numerical simulations . The upper part is the anode separated from the hollow cathode by an insulator . In addition, the position of the Langmuir-probe in the hollow cathode is shown . The optical path is drawn in radially enlarged at the ams .
0168-9002/90/$03 .50 (0 1990 - Elsevier Science Publishers B .V . (North-Holland)
412
C. Schuitheiss et al. / Investigation andsimulation ofprebreakdown
Fig. 2. Total current of the pseudospark discharge (t = 0 when the voltage drops to i of its maximum value) . Two lines were investigated which are excited with sufficient strength in the discharge. The strongest is the 391 .4 nm N2 II-ion line; the second one is the 632.2 rum excitation of N2 I. Both lines are band heads of the First Negative System which appears typically in lowpressure discharges. The intensity of the neutral line is about 20 times lower than that of the strongest ion line. Fig. 1 shows the chamber which consists of ~n anode/cathode gap and a hollow cathode region . The depth of the hollow cathode as well as the anode cathode gap is 10 mm; the diameter of the axial bore hole is 5 mm and the disc thickness is 4 mm. In addition the position of a floating Langmuir probe is shown,
Fig. 3. Current detected by the floating Langmuir probe with an active area of 50 mm2 (time-scale : see fig. 2).
Fig. 4. Time development of the intensity of the 391 .4 nm nitrogen line measured on the axis (time-scale : see fig. 2) .
C. Schultheiss et al. / Inwstigation and simulation ofprebreakdown
which was used to give an early trigger signal to the optical spectral multichannel analyser (OSMA, spectral resolution : 1 .59 nm/mm, focus length 0.5 m, time resolution 12 ns). Furthermore, fig . 1 shows the light cone accepted by the optical system. Within a solid angle of 1 .02 x 10-° sr light passes a quartz window at the bottom of the hollow cathode, crosses the optical system and reaches the diode array at the exit of the spectrometer. The optical system has a focus diameter of 100 pm; the cone opens at the quartz exit to 285 pm. To vary the radial position of the optical path, the chamber itself can be shifted radially by means of a micrometer system . The step width is 0.2 mm. Since the optical paths overlap between the step widths, an unfolding procedure was necessary afterwards. The pseudospark chamber was connected with a 1 nF capacitor and charged via a resistance to 6 kV. In the self-breakdown mode at a pressure of 10 Pa the measurements were carried out with a repetition frequency of about 20 Hz. Fig. 2 shows the total discharge current as a function of time. For the experimental analysis the time zeropoint is defined as the time, at which the applied voltage has dropped to 1' . Fig . 3 gives a logarithmic plot of the current detected by the floating Langmuir probe also as a function of time. Here a feature typical for the pseudospark can be observed : The probe current has a positive polarity from the very beginning. In LTE
105 El
N c ar c
413
Radius
( cm I
Fig. 6. Intensity of the 632 .2 rim nitrogen I line as a function of radius and time (time-scale: see fig . 2).
plasmas the polarity normally is negative . Further, the usual zero balancing of the probe current by means of an applied bias voltage is not possible for times later than -200 ns. Obviously the Langmui: theory of a floating probe fails in our case. This may be explained by the fact that in addition to a flow and counterflow of electrons and ions to the probe it is also irradiated by photons with an energy in the order of 100 eV . This VUV radiation causes a loss of electrons due to the photo effect which is responsible for the positive charge of the probe. Fig . 4 shows as an example the time development of the 391 .4 rim line of nitrogen ions in the region between -100 ns and + 150 ns directly on the axis. Because of a too low light intensity, it was not possible to obtain spectra in the time region before -100 ns although up to 20 single measurements were added . The same can be stated for the 632 .2 rim line, for which the earliest signal could be measured 60 ns ahead of the time zero-point . Figs. 5 and 6 summarize the analysis (id ih e ni sured photon flux density for different radii and times of the two nitrogen lines. All intensity plots show a peak between the axis and r = 0.2 mm, which means with a that in this integration interval a central b radius r < 0.2 mm is embedded. A systematic dip of the measured point at r = 0.2 mrn results from the unfolding procedure mentioned above. n
10 1 '
e
0.0
e
.
I . 0.1
t
s
I . . . A . 0.2 0.3
t
-
I
e
0.4
-
i I . i I 0.5 0.6
Radius
e
[cm l
e
t
0.7
Fig. 5. Intensity of the 391 .4 rim nitrogen II line as a function of radius and time (time scale: see fig. 2).
_a
C: Schultheiss et al. / Investigation and simulation ofprebreakdown
414
3. Numerical simulation of the prebreakdown in a hollow cathode geometry 3.1. Simulation parameters The simulations were performed for the geometry shown in fig. 1. The voltage taken was 6 kV, constant in time, which equals the peak voltage in the experiments described above . In order to observe an ionization growth in the simulations the pressure had to be chosen larger than in the experiments, namely 130 Pa. In addition, a high photon secondary coefficient of 0.4 was required to produce enough secondary electrons to yield a growth in densities. From the discrepancy with respect to the onset of ionization growth between experiments and simulation, it follows that some major causes for charge carrier muiiipiication are missing in the model. The reason is that all discharge physics in the hole and gap regions are neglected. Therefore, the effect of slow and fast ions, or fast neutrals hitting the disc in the hole region releasing secondary electrons there, as well as the secondary electrons from the light produced in the gap between anode and cathode are missing. Also, fast ions (or neutrals after charge exchange) having gained energy in the keV range in the anode-cathode gap, passing through the HCR fast, then hitting the wall opposite the hole may release a significant fraction of secondary electrons . For example, it was shown, that such a fast ion flux with a current density of only 1/100 of that of the electrons leaving the hole was equivalent to reducing the required photon secondary coefficient by a factor of 20. 3.2. Results of the simulations
influence is still negligible . The initial low level electron density is assumed to be uniform in space, and the ion density is taken to be zero. The total electron current leaving the HCR is shown as a function of time in fig. 7. The electron current density at the hollow boundary across the hole is shown in fig. 8, with the time as parameter. At time zero the
N z= U c-+
v
x
In the theoretical analysis the time zero is defined at the begin of the simulation at which the space charge --3 .
z 0 0 v J
v
z w
Fig. 8. Electron current density at the hollow cathode boundary across the hole with time as parameter (time-scale : see fig. 7).
-q .
I
:5 -5 .
0
LL.11_:-LU1~
200
q00
L~
1 ' ' . ._L ' . ' ' '
600
800 1000 TIME (N5)
Fig. 7. Total electron current leaving the hole as function of time (t = 0 at the start of the simulation) .
Fig. 9. Photon flux density at the end wall in the hollow cathode region as a function of radius with time as parameter, integrated over an 0.2 mm optical channel perpendicular to the end wall (time-scale : see fig. 7).
C. Schuitheiss et al. / Investigation and simulation oferebreakdown
initial electrons start to move, producing secondary electrons and ions by impact ionization in the volume. Exitation and photon emission causes secondary electrons at the walls in the HCR. After about 20 ns the initial electrons have left the HCR through the hole, and a self-consistent solution of the equations remains . This effect is seen in figs. 7 and 8 initially. Next follows a period in time during which the growth in current and densities is exponential. During a transition phase, the growth rate gets gradually overexpontial across all of the hole. During this phase, the positive ion space charge inside the HCR starts to change the electric field . Finally, during a very short time of only several ns, the growth in current density in the vicinity of the axis explodes, and a high current density, small diameter electron beam leaves the HCR . At this time the total electron current leaving the hole is of the order of a mA. The photon flux density at the end wall in the HCR is shown in fig. 9 as a function of radius with time as parameter . In order to be comparable to the experiments reported above, the light originating inside the HCR in a cylinder of 0.2 mm diameter, perpendicular to the end wall, was integrated. 4. Matching of the simulation- and experimental time scale To compare the experimental results with those of the numerical simulation, one has to keep in mind that the simulation starts at a time for which the space charge influence is negligible, and ends at the onset of the current instability, whereas the spectroscopical experiment starts at the first observable light emission and ends at the beginning of the main discharge . The relation between the different time scales can be found by an estimation of the observed photon flux density. Assuming a spectrometer opening time of 12 ns, a number of 500 photons as statistical observation limit, 4 channels as detector resolution, about 10 lines over which was integrated and putting in the actual geometrical properties a photon flux density of 6 x 102° (scm2)-1 is estimated as the observation limit. This is more than 1018 (s cm2 )-1 ; the value reached in the simulation . From this argument we have to conclude, that the measurements start at some time aiier thc simulation had already ended. The simulation ends at 962 ns; from fig . 9 one concludes, that on the average the light emission in the hollow cathode approximately increases by a factor of 10 every 20 ns. Extrapolating, the photon flux density in the hollow cathode would reach the experimental threshold value of 6 x 102° about 100 ns later, which means at a simulation time 1060 ns. thus the time difference between the end of the simulation and the time zero of the experiment (see figs. 4 and
41 5
Time t ns I Fig. 10. Overview on the measurements and a comparison with the total current of the simulation on the common time scale determined . A time gap of about 100 ns separates the end of the simulation and the beginning of the visible light detection. The VUV detection (Langmuir probe) extends into both time scales and shows a transition behaviour just at the time where the simulation ends. The total current of the simulation is scaled to match the VUV curve in one point. 5) is about 200 ns. This can be confirmed by extrapolating the experimentally observed total current (fig. 2) back to a level of 1 mA at which the simulation was stopped (see fig . 7). Fig. 10 shows a summary of the measurements and the total current of the simulation on the common time scale just determined . The logarithmic ordinate is in arbitrary units. Since the average light emission is proportional to the average current of the simulation the current is adapted to the VUV radiation curve by applying a scale factor. In the next section fig. 10 will be discussed in detail . 5. Comparison of simulation and ex
riment
of the wh-n nsav densities 1!t ..~.... .., 51 14V111PW1JV11 VA L114 tliel3EVS6 ®eas e densities a.. fig's
6 and 9 shows that simulation and experiment agree qualitatively. The sharp maximum of the light intensity on the axis and its radial decrease into the hollow cathode area are similar in the experiment and in the simulation . This is an important result because the simulation predicted that the onset of the pseudospark happens on the axis close to the hole, and this is in accordance with our experimental results . This measurement also agrees with side-on streak measurements for a
416
C. Schultheiss et al. / Investigation andsimulation ofprebreakdown
one-gap pseudospark chamber [8] where the first light emission was observed in a small area on the axis at the exit of the hollow cathode. From fig. 10 it can be seen that except for the Langmuir probe measurement no time overlap between experimental measurements and simulation exists and therefore the theoretically predicted overexponential rise of the visible photon flux could not be observed experimentally in principle. The time development of the total current in the simulation during the overexponential rise and the increase of exponential growth of the early signal of the Langmuir probe can be interpreted as a change of the discharge properties : The onset of VUV radiation indicates that an increasing amount of electrons become run-away and start to generate bremsstrahlung and K-radiation in the working gas. This means that the fluid model of the simulation starts to fail since the movement of the electrons is no longer determined by the local electric fields only . After this change of discharge properties, both the VUV and the visible light intensity grow exponentially again . For this discharge phase another physical model is required [9]. In addition, it must be recalled that there is a difference in the pressure. :f the experiments are operated at the pressure used in the simulation (p =130 Pa), no pseudospark would appear. On the other hand, with the experimental pressure (p = 10 Pa) the simulation shows an exponential decay of the initial charge densities rather than a buildup of the discharge. This is not surprising, since in the real experiment a number of effects contribute to the production of charge carriers which are not included in the model, e.g. enhanced emission from surfaces due to adsorbates, as well as light, fast neutrals and ions coming from the main gap into the hollow cathode.
With these restrictions in mind it is fair to state that the experiments support the results of the simulations.
Acknowledgements Stimulating discussions with A. Citron, A.J. Davies, W. Hartmann, W. Niessen, P. Choi and W. Schmidt were valuable and encouraging for this work.
References [11 J. Christiansen and Chr. Schultheiss, Z. Phys. A290 (1979) 35 .
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