- Email: [email protected]
Pressure jump across normal ionizing shock waves
Volume 40A, number 5
PHYSICS LETTERS
14 August 1972
PRESSURE JUMP ACROSS NORMAL IONIZING SHOCK WAVES* P.H. NITSCHKE, M.H. BRENNAN and M.G.R. PHILLIPS School o f Physical Sciences, The Flinders University of South Australia, Bedford Park, S.A. 5042, Australia Received 6 March 1972 The pressure jump across normal ionizing shock waves in hydrogen has been measured using piezoelectric probes. The observed pressure jumps exhibit substantial radial variations with average values higher than those predicted by theory.
Measurements of the pressure jump across normal ionizing shock waves have been made using fast-response piezoelectric probes. The experiments were performed in the plasma source FPS 1, described by Blackburn et al. [ 1 ]. In this device the shock is formed by an approximately square current pulse flowing between two electrodes in a cylindrical geometry. The electrodes used were a short centre electrode, 15 cm long and 2.8 cm in diameter, and an outer electrode of 9.5 cm inner diameter which extended for the whole length of the shock tube; the "hybrid configuration" described by Blackburn et al. [ 1]. The experiments were performed in hydrogen at an initial neutral gas pressure of 150 m torr and with a steady axial magnetic field of 5.5 kG. The shock drive current and velocity were measured using small pick-up coils oriented to detect the bo-component of the drive field. The pressure probes used were of the acoustic delay line type described by Biichl [2], with a disc of piezoelectric material (PZT-4) mounted between two quartz rods of 1 mm diameter and 10 cm in length. The front quartz rod, which is inserted into the plasma, delays the pressure signal until after the electrical noise from the shock tube has ceased. The length of the second rod provides a useful observation time of about 40/as. The probes were tested by placing the tip flush with the wall of a gas dynamic diaphragm shock tube [3] and comparing the probe signal with the computed pressure jump. The probes were found to have a linear response over the pressure range of interest.
The probes were inserted radially into FPS I at a position 75 cm from the launching electrode. Calculations of the radial particle velocity, which are supported by Doppler shift measurements, indicate that the contribution that this directed flow makes to the probe signal can be ignored. Typically, the pressure was observed to rise in ~ 1/as after the arrival of the shock front (presumably corresponding to the risetime of the probe itself) and to remain essentially constant over the observation time of 40/as. Fig. 1 shows the radial variation in the pressure for four shock velocities corresponding to drive currents in the range 10 to 42 kA. One notes the expected low pressures in the shadow of the central electrode and, in addition, the substantial radial variations in pressure over the shock-heated region between the two electrodes. At the highest shock velocity observed in the pres-
*This work was supported by the Australian Research Grants Committee and the Australian Institute of Nuclear Science and Engineering.
Fig. 1. Radial variation of pressure jump for four shock speeds: (o 1.6, X 3.0, A3.9, t3 5.0) X 104 ms-1 . Shaded regions indicate electrode positions.
8 I~IIIIIIIIA
il 0 0
1
2
3
4
5
Rad~L position (crrO
367
Volume 40A, number 5
PHYSICS LETTERS
Table 1 Dependence of pressure jump on shock velocity Velocity (10 4 ins -I )
Pressure (theory) (10 3 Nm -2)
1.6 3.(1 3.9 5.0
5.2 8,4 13.8
1.6
Pressure (exp.) (10 3 Nm -2) 8.3 17 24 32
ent experiments the post-shock plasma is essentially fully ionized; the ion and electron temperatures rapidly become equal, in a time much less than the risetime of the pressure probe signal. The post-shock pressure is thus ~ 2 nkT, where n and T are the electron density and temperature. It was therefore possible to calibrate the pressure probe by comparing its response with the pressure determined from the electron density and temperature obtained from a laser scattering measurement at r = 2.8 cm, Using this calibration we compare, in table 1, the pressure j u m p predicted by the theory of James [4] with the aver-
3~
14 August 1972
age pressure measured in the shock-heated region. One notes that the measured pressures are considerably higher than the theoretical predictions. It is possible that the discrepancy between theory and experiment, which is most marked at low shock velocities, may be due, in part, to a variation in probe sensitivity with shock velocity, arising from a different sensitivity to charged and neutral particles or from differences in the flow pattern around the probe tip. On the other hand, the substantial radial variations in the observed pressures are not likely to be so sensitive to these effects; they clearly demonstrate the inadequacy of the present one-dimensional theories in which radial variatons in the azimuthal drive field are ignored.
References [1] T.R. Blackburn, M.H. Brennan and J. Fletcher, Plasma Phys. 11 (1969) 655. [2] K. Biichl, Z. Naturforsch. 19a (1964) 690. [3] M.G.R. Phillips and C.A. Harris, Rev. Sci. Instr., to be published. [4] B.W. James, Phys. Lett. 9 (1969) 509.
PHYSICS LETTERS
14 August 1972
PRESSURE JUMP ACROSS NORMAL IONIZING SHOCK WAVES* P.H. NITSCHKE, M.H. BRENNAN and M.G.R. PHILLIPS School o f Physical Sciences, The Flinders University of South Australia, Bedford Park, S.A. 5042, Australia Received 6 March 1972 The pressure jump across normal ionizing shock waves in hydrogen has been measured using piezoelectric probes. The observed pressure jumps exhibit substantial radial variations with average values higher than those predicted by theory.
Measurements of the pressure jump across normal ionizing shock waves have been made using fast-response piezoelectric probes. The experiments were performed in the plasma source FPS 1, described by Blackburn et al. [ 1 ]. In this device the shock is formed by an approximately square current pulse flowing between two electrodes in a cylindrical geometry. The electrodes used were a short centre electrode, 15 cm long and 2.8 cm in diameter, and an outer electrode of 9.5 cm inner diameter which extended for the whole length of the shock tube; the "hybrid configuration" described by Blackburn et al. [ 1]. The experiments were performed in hydrogen at an initial neutral gas pressure of 150 m torr and with a steady axial magnetic field of 5.5 kG. The shock drive current and velocity were measured using small pick-up coils oriented to detect the bo-component of the drive field. The pressure probes used were of the acoustic delay line type described by Biichl [2], with a disc of piezoelectric material (PZT-4) mounted between two quartz rods of 1 mm diameter and 10 cm in length. The front quartz rod, which is inserted into the plasma, delays the pressure signal until after the electrical noise from the shock tube has ceased. The length of the second rod provides a useful observation time of about 40/as. The probes were tested by placing the tip flush with the wall of a gas dynamic diaphragm shock tube [3] and comparing the probe signal with the computed pressure jump. The probes were found to have a linear response over the pressure range of interest.
The probes were inserted radially into FPS I at a position 75 cm from the launching electrode. Calculations of the radial particle velocity, which are supported by Doppler shift measurements, indicate that the contribution that this directed flow makes to the probe signal can be ignored. Typically, the pressure was observed to rise in ~ 1/as after the arrival of the shock front (presumably corresponding to the risetime of the probe itself) and to remain essentially constant over the observation time of 40/as. Fig. 1 shows the radial variation in the pressure for four shock velocities corresponding to drive currents in the range 10 to 42 kA. One notes the expected low pressures in the shadow of the central electrode and, in addition, the substantial radial variations in pressure over the shock-heated region between the two electrodes. At the highest shock velocity observed in the pres-
*This work was supported by the Australian Research Grants Committee and the Australian Institute of Nuclear Science and Engineering.
Fig. 1. Radial variation of pressure jump for four shock speeds: (o 1.6, X 3.0, A3.9, t3 5.0) X 104 ms-1 . Shaded regions indicate electrode positions.
8 I~IIIIIIIIA
il 0 0
1
2
3
4
5
Rad~L position (crrO
367
Volume 40A, number 5
PHYSICS LETTERS
Table 1 Dependence of pressure jump on shock velocity Velocity (10 4 ins -I )
Pressure (theory) (10 3 Nm -2)
1.6 3.(1 3.9 5.0
5.2 8,4 13.8
1.6
Pressure (exp.) (10 3 Nm -2) 8.3 17 24 32
ent experiments the post-shock plasma is essentially fully ionized; the ion and electron temperatures rapidly become equal, in a time much less than the risetime of the pressure probe signal. The post-shock pressure is thus ~ 2 nkT, where n and T are the electron density and temperature. It was therefore possible to calibrate the pressure probe by comparing its response with the pressure determined from the electron density and temperature obtained from a laser scattering measurement at r = 2.8 cm, Using this calibration we compare, in table 1, the pressure j u m p predicted by the theory of James [4] with the aver-
3~
14 August 1972
age pressure measured in the shock-heated region. One notes that the measured pressures are considerably higher than the theoretical predictions. It is possible that the discrepancy between theory and experiment, which is most marked at low shock velocities, may be due, in part, to a variation in probe sensitivity with shock velocity, arising from a different sensitivity to charged and neutral particles or from differences in the flow pattern around the probe tip. On the other hand, the substantial radial variations in the observed pressures are not likely to be so sensitive to these effects; they clearly demonstrate the inadequacy of the present one-dimensional theories in which radial variatons in the azimuthal drive field are ignored.
References [1] T.R. Blackburn, M.H. Brennan and J. Fletcher, Plasma Phys. 11 (1969) 655. [2] K. Biichl, Z. Naturforsch. 19a (1964) 690. [3] M.G.R. Phillips and C.A. Harris, Rev. Sci. Instr., to be published. [4] B.W. James, Phys. Lett. 9 (1969) 509.