Experimental Observation of Further Frequency Upshift from dc to ac ...

VOLUME 85, NUMBER 21

PHYSICAL REVIEW LETTERS

20 NOVEMBER 2000

Experimental Observation of Further Frequency Upshift from dc to ac Radiation Converter with Perpendicular dc Magnetic Field T. Higashiguchi, N. Yugami, H. Gao, T. Niiyama, S. Sasaki, E. Takahashi, H. Ito, and Y. Nishida Department of Energy and Environmental Science, Graduate School of Engineering, Utsunomiya University, Utsunomiya, Tochigi 3218585, Japan (Received 1 March 2000) A frequency upshift of a short microwave pulse is generated by the interaction between a relativistic underdense ionization front and a periodic electrostatic field with a perpendicular dc magnetic field. When the dc magnetic field is applied, further frequency upshift of 3 GHz is observed with respect to an unmagnetized case which has typically a GHz range. The radiation frequency depends on both the plasma density and the strength of the dc magnetic field, i.e., the plasma frequency and the cyclotron frequency. The frequency of the emitted radiation is in reasonable agreement with the theoretical values. PACS numbers: 52.75.Va, 41.60.– m, 84.40.–x

The interaction between a moving gas/plasma boundary and the electromagnetic (EM) wave has been studied for plasma applications of the plasma-based radiation source or tunable radiation source [1–5]. The frequency upshift of the EM wave with the laser produced underdense ionization front having a speed of light was studied by Mori in 1991 [4]. This phenomenon of the frequency upshift is the phase modulation of the incident wave by the ionization front. Savage et al. studied experimental frequency upshift of the microwave frequency from 35 GHz to over 170 GHz by using the laser produced underdense ionization front in 1993 [6]. The frequency upshift can also be expected from a periodic electrostatic field instead of the initial EM wave, because the periodic electrostatic field is observed as the incident EM wave with the frequency of v 0 ﬁ 0 in the frame moving with the ionization front. In the laboratory frame, the transmitted wave in the plasma behind the ionization front is directly observed as the EM wave radiation pulse. The observed frequency, however, is upshifted from zero frequency, that is, this scheme can directly convert the dc field energy to the EM wave radiation. This phenomenon is called “RIFLE” [7] (radiation from interaction of ionization front with lined electrostatic field) and used to be DARC (dc to ac radiation converter) [8–14]. Advantages of the RIFLE are as follows: (1) a short EM pulse (a few cycles), (2) frequency tunability (GHz – THz), (3) high power, and (4) a simple device. The RIFLE is one of the frequency upshift phenomena, and the experimental confirmation has been reported for the unmagnetized plasma [9–14]. The frequency of the emitted radiation from the RIFLE depends on the plasma density for the fixed wavelength of the periodic electrostatic field. In this Letter, we wish to present the experimental results of further frequency upshift of the RIFLE when applying the perpendicular dc magnetic field to the electrostatic field area. This phenomenon is expected from the dispersion relation of the EM wave in the magnetized plasma, where a higher frequency branch than the unmagnetized plasma 4542

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can exist. By magnetizing the plasma in the RIFLE, we observed a higher frequency than that of the unmagnetized case in the X-band region. In the RIFLE with/without the static magnetic field (shown in Fig. 1), a sinusoidal electrostatic field Ey 艐 E0 sink0 x (v0 苷 0, k0 苷 2p兾2d) is excited by an alternately biased electrode array with the separation distance of d. The velocity of the ionization front (yf ) propagates in the 1x direction with the group velocity yf determined by an ionizing laser pulse in the plasma and is approximately equal to the speed of light, i.e., yf 苷 c共1 2 vp2 兾 vL2 兲1兾2 艐 c, where c, vp , and vL are the speed of light, the plasma frequency, and the laser frequency, respectively. To explain the radiation mechanism of the short EM wave pulse, we consider in the reference frame moving with the ionization front. In the front frame, the periodic electrostatic field is observed like an incident EM wave with the frequency of v 0 苷 gk0 yf , where g 艐 vL 兾vp is the relativistic factor of the ionization front and a prime denotes the front frame quantities. For v 0 . vp , the EM wave is transmitted in the plasma behind the ionization front, where vp is the Lorentz invariant. The transmitted wave satisfies the dispersion relation of v 0 2 苷 vp2 1 c2 k 0 2 in the plasma. The frequency of the emitted radiation is given by Eq. (1) [8]: v 苷 g k0 yf 2

µ ∂1兾2 ∏ vp2 yf 12 2 2 2 12 . c g k0 yf

∑

(1)

Lai et al. [15] proposed further frequency upshift by the interaction between the ionization front and the EM wave when the dc magnetic field is applied to the plasma. On the RIFLE, the initial EM wave could be replaced by the periodic electrostatic field, and further frequency upshifts of the emitted radiation are expected as the extraordinary mode (X-mode) at v . vR . vp , when a perpendicular dc magnetic field is applied to the RIFLE, where vR is the cutoff frequency of the right-hand polarized mode © 2000 The American Physical Society



Radiation Ionization Front

-

Ionizing Laser

+

-

Plasma

E0

B0

y +

z

-

+

d

x

-

vf +

-

+

Static E Field

FIG. 1. Schematic of the RIFLE apparatus. The ionization front propagates in the 1x direction. A periodic electrostatic field is applied in the y direction. Output radiation propagates in the 1x direction.

(R branch). The output frequency from the RIFLE with the perpendicular dc magnetic field can be estimated by using the Lorentz transformation in the same way as the case without the dc magnetic field. In the frame moving with the ionization front, the periodic electrostatic field is given by Ey0 艐 g共E0 sinf 1

20 NOVEMBER 2000

cB0 兲 and Bz0 艐 2g关B0 1 共E0 兾c兲 sinf兴, where f 苷 f 0 苷 k 0 x 0 1 v 0 t 0 , and yf 兾c 艐 1. Since the second term of B0z can be neglected compared to the first term for E0 兾c ø B0 , the strength of the magnetic field is Bz0 艐 gB0 . The electron cyclotron frequency is the Lorentz invariant because vc0 苷 eB0z 兾m0 艐 egB0 兾gm 苷 vc . Therefore, each frequency of vR兾L and vh is approximately Lorentz invariant, where the cutoff frequencies of vR兾L and the upper hybrid frequency of vh are defined as vR兾L 苷关6vc 1 共vc2 1 4vp2 兲1兾2 兴兾2 and vh2 苷 vc2 1 vp2 , respectively. The dispersion relation of the EM wave in the front frame with the perpendicular dc magnetic field is given as in Ref. [16] vp2 v 0 2 2 vp2 c2 k 0 2 . (2) 苷 1 2 v0 2 v 0 2 v 0 2 2 vh2

The frequency of the transmitted wave in the magnetized plasma behind the ionization front is equal to v 0 . The transmitted wave must satisfy Eq. (2). We can finally obtain the output frequency of the emitted radiation after transforming back to the laboratory frame, ∑ Ω µ ∂∏1兾2 æ vp2 yf vc2 2 12 2 2 2 11 2 2 2 v 苷 g k0 yf 1 2 . (3) c g k0 yf g k0 yf 2 vh2

For the unmagnetized case, i.e., vc 苷 0 and vh 苷 vp , Eq. (3) is identical to Eq. (1). The frequency of the emitted radiation can be directly estimated by using the dispersion relation and the phase continuity relation v 1 kyf 苷 k0 yf between the periodic electrostatic field and the radiation at the ionization front boundary. The frequency of the emitted radiation is given by the intersection between two conditions in the laboratory frame. Figure 2 shows the dispersion relation (O-mode, X-mode) and the phase continuity equation. Thus, further frequency upshift of the emitted radiation from the RIFLE can be expected by applying the perpendicular dc magnetic field. For example, for the plasma density np 苷 1 3 1012 cm23 , B0 苷 2 kG, and 2pc兾vL 苷 266 nm, we can estimate the incident frequency to the ionization front equal to v 0 兾2p 苷 gk0 yf 兾2p 苷 1.5 3 1015 Hz and the upper cutoff frequency to vR 兾2p 苷 1.3 3 1010 Hz for 2d 苷 2 cm. Thus, the relation satisfies v 0 . vR . vh . The frequency of the emitted radiation is connected to the R branch of the extraordinary mode to satisfy v . vR . vp and further frequency upshift of the emitted radiation can be expected, such as the frequency “A” without the magnetic field to “B” with the static magnetic field in Fig. 2. In our experimental parameters at np 苷共1 10兲 3 1011 cm23 and B0 苷 400 2000 G, further frequency upshift of several GHz is expected compared to an unmagnetized case. In the experiment, the electrode array for exciting the periodic electrostatic field consists of N 苷 6 periods (i.e., 13 electrode pairs) and the distance between the adjacent electrodes is d 苷 1 cm with a gap of b 苷 0.6 cm. This

electrode structure is set in the waveguide with a cutoff frequency of vcw 兾2p 苷 6.55 GHz for TE10 mode. The electrostatic field is excited by the pulsed power supply with a maximum bias voltage of 5 kV and a pulse width of 2 ms. One electrode array is supplied with high voltages and the other is connected to the ground. A working gas is TMAE (tetrakis-dimethyl-amino-ethylene: C10 H24 N4 ) with the ionization potential of Ui 苷 5.36 eV. This material vaporizes at room temperature and is easily ionized by UV laser light. The laser pulse has a width of tL 苷 6 ns in FWHM, a spot diameter of 1 cm, and a total energy of 100 mJ. The plasma density is a function of the TMAE gas pressure and the laser energy. The plasma density as a function of the TMAE gas pressure is measured

=-ck

X-mode

B

R

=ck h

O-mode

A

X-mode

p L

0

k0

k

FIG. 2. Dispersion relation of the EM wave in the plasma with/without a perpendicular dc magnetic field. The dotted curve is for the unmagnetized case, i.e., the EM wave propagates as the ordinary mode (O-mode) in the plasma. For the magnetized case, the EM wave propagates as the extraordinary mode (X-mode) in the plasma.

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8 GHz

14

P = 5 mTorr -0.2 L = 2900 cm

-0.4 -0.6 -0.8 -1 -1.2

9.7 GHz

0

50

100

8.9 GHz

150

200

FIG. 3. Typical waveforms of the delayed signal through the delay waveguide line with the length of L 苷 2900 cm with/without a dc magnetic field (800 G: solid line/0 G: dotted line) at the TMAE gas pressure of 5 mTorr. The intensities of delayed waveforms are normalized to their peak value. The center frequencies are 9.7 and 8.9 GHz, respectively.

(Th.) 2 kG 800 G 340 G 0G

12 10 9.5

8 6 0G 340 G 800 G 2 kG

4 2 0

0

2

Frequency (GHz)

0

Delayed Time (ns)

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magnetic field from each waveform. In this case, the frequency upshift of 0.8 GHz is observed. Figure 4 shows examples of the experimental result of the observed center frequency of the emitted radiation as a function of the plasma density. The perpendicular dc magnetic field is applied to the RIFLE structure with a strength between 0 and 2 kG. The plotted dots are the average values of the experimental 5 data, and the horizontal and vertical error bars indicate the standard deviation of the plasma density and the observed frequency, respectively. The observed frequency increases with both the plasma density and the strength of the dc magnetic field. The solid line shows the theoretical value for d 苷 1 cm with/without the perpendicular dc magnetic field. Since the rise time of the plasma density is almost the same with the laser pulse width 6 ns, we think that the invalidity of the sharp front assumption is the reason for the disagreement between the experiment and the theory. Figure 4 shows very weak dependence of the frequency on the plasma density at B0 苷 0 G. The expected radiation frequency is 8.1– 9.4 GHz for the plasma density of 2.3 3 1011 7 3 1011 cm23 , that is, this corresponds to several hundred MHz increment. The experimental result is from 8.5 to 9 GHz. The frequency change is smaller than the expected values, but the observed frequencies really depend on the plasma density and are approximately equal to the theoretically expected values. The inset in Fig. 4 shows the emitted frequency at B0 苷 0 G versus the plasma density in expanded scale in frequency showing the reasonable agreement with the theoretical one. The observed frequencies v 苷 v共np , B0 兲 are tunable and in reasonable agreement with the one determined by the plasma density and the strength of the dc magnetic field. It

Frequency (GHz)

Normalized Delay Signal

14 GHz 11 GHz 10 GHz 9 GHz

by both the 24 GHz microwave interferometer and the 9 GHz reflectometer (corresponding to the critical density of 1 3 1012 cm23 ). The emitted radiation is detected by the crystal detector with a temporal resolution of less than 1 ns. The center frequency of the emitted radiation is measured by employing the time-of-flight (TOF) method with the delay waveguide line of the cutoff frequency of vcw 兾2p 苷 6.55 GHz for TE10 mode. The spectrum analyzer is popularly used for the frequency measurement, but it has poor time resolution. The TOF method, however, has the principle that the group velocity has frequency dependence in the waveguide [17]. The group velocity in the waveguide is 2 given by yg 苷 c共1 2 vcw 兾v 2 兲1兾2 . The time response is much better than the conventional spectrum analyzer. In this system, the frequency of the emitted radiation can be analyzed by measuring the delay time of the pulse. The delay time of the packet is given by td 共v兲苷 L兾yg 共v兲 when the EM wave packet travels in the waveguide with a length of L. Thus the emitted frequency from the RIFLE is given by v 苷 vcw ctd 兾共c2 td2 2 L2 兲1兾2 . Figure 3 shows an example of two delayed waveforms through the delay waveguide line in the frequency measurement at the TMAE gas pressure of 5 mTorr. The delayed time or the time of flight is much longer than the initial pulse width of the emitted radiation. The solid line and the dotted one are with/without the dc magnetic field (800 G/0 G), respectively. Two observed delay times of td 苷 131.6 and 142.6 ns correspond to center frequencies of 9.7 and 8.9 GHz, respectively, with/without the

20 NOVEMBER 2000

9

8.5

8

B0 = 0 G 0

2

4

6

8

10

Density (x1011 cm -3 )

4

6 11

Density (x10

8

10

-3

cm )

FIG. 4. Center frequencies of the emitted radiation from the RIFLE as a function of the plasma density with the parameters of the perpendicular dc magnetic field. The solid line is the theoretical line. The inset shows the result without the magnetic field B0 .


affords the possibility of externally controllable parameters in a laboratory experiment. In our future task, we would like to use a much shorter laser pulse in our experiments. Lai and co-workers have also discussed the transmission coefficient at the interaction boundary between the EM wave and the ionization front in the magnetized plasma [15]. The increment of the output power has not been observed because the magnetic field provides no energy into the system. Strictly speaking, the transmission coefficient of the emitted radiation is not equal to unity because there exists the free streaming mode which stores the energy depending on the magnetic field. The observed radiation undertakes the X1 -mode in Ref. [15]. The transmission coefficient of the X1 -mode decreases with the increase of vc 兾vp . In Fig. 5, the ratio PB 兾P0 of the observed power of the emitted radiation with the dc magnetic field B0 to that without B0 is shown as a function of the applied bias voltage, where PB and P0 are the output powers with/without the magnetic field, respectively. According to Ref. [15], the ratio of the transmission coefficient is TB 兾T0 艐 0.9 at B0 苷 800 G and np 苷 6.3 3 1011 cm23 (correspondent to vc 兾vp 艐 0.3), where TB and T0 are the transmission coefficients of the emitted radiation with/without the magnetic field. The experimental result of PB 兾P0 艐 0.9 1 and this value of the ratio is reasonable. We did not calibrate the crystal detector to the absolute microwave power, but the observed output power was estimated to be several hundred milliwatts. The reason for the power shortfall is due to the long front length in our present experiments, as well as the microwave technique, such as the RIFLE structure in the waveguide does not properly couple to the radiation region and the measurement system. The rise time of the laser is so long that the emission starts to gradually deplete the stored electrostatic energy. If in an ideal way the laser rise time is negligibly small the emission is concentrated into the expected pulse width, which should be in picosecond order. In this situation the output power could become the expected values. However, the observed output power is experimentally proportional to the bias voltage with the power of 2 and shows reasonable agreement with the theoretical prediction [13]. In conclusion, further frequency upshift from the RIFLE structure with the perpendicular dc magnetic field is observed. The frequency of the emitted radiation is measured by the TOF method of the delay waveguide line. The observed frequencies with/without the dc magnetic field (2 kG/0 kG) are 10–12 GHz and 8 –9 GHz in the 1011 cm23 range, respectively. The observed frequency depends on both the plasma density and the strength of the dc magnetic field and is in reasonable agreement with the predicted theoretical value. We would like to acknowledge useful discussions with H. Okabe. A part of the present work was supported by

20 NOVEMBER 2000

1.5

PB /P0


1

0.5 0 0.5

1

1.5

2

2.5

3

Bias Voltage (kV) FIG. 5. Normalized output power PB 兾P0 of the emitted radiation from the RIFLE as a function of the applied bias voltage, where PB (B0 苷 800 G) and P0 (B0 苷 0 G) are the output powers with/without the dc magnetic field, respectively. The solid line is the expected value PB 兾P0 苷 0.9.

a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan. One of the authors (T. H.) is also grateful to the JSPS Research Fellowships for Young Scientists. We also are grateful to the Cooperative Research Center and the Satellite Venture Business Laboratory (SVBL) of Utsunomiya University for providing the laser system.

[1] [2] [3] [4] [5] [6] [7]

[8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

M. Lampe et al., Phys. Fluids 21, 42 (1978). M. D. Perry et al., Phys. Rev. A 37, 747 (1988). S. C. Wilks et al., Phys. Rev. Lett. 61, 337 (1988). S. C. Wilks et al., Phys. Rev. Lett. 62, 2600 (1989). W. B. Mori, Phys. Rev. A 44, 5118 (1991). R. L. Savage et al., IEEE Trans. Plasma Sci. 21, 5 (1993). The term “DARC” is a misleading description of the phenomena of the present system, because most radiation systems have a principle to convert dc energy to ac energy, i.e., the e-beam energy in most microwave sources is converted to radiation. Therefore, we made a new nickname RIFLE which is a more appropriate term to describe the phenomena. W. B. Mori et al., Phys. Rev. Lett. 74, 542 (1995). C. H. Lai et al., Phys. Rev. Lett. 77, 4764 (1996). P. Muggli et al., Appl. Phys. Lett. 72, 19 (1998). P. Muggli et al., Phys. Plasmas 5, 2112 (1998). N. Yugami et al., Jpn. J. Appl. Phys. 37, 688 (1998). T. Higashiguchi et al., Jpn. J. Appl. Phys. 38, L527 (1999). T. Higashiguchi et al., Bull. Am. Phys. Soc. 44, 240 (1999). C. H. Lai et al., IEEE Trans. Plasma Sci. 21, 45 (1993). F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, 1 (Plenum Press, New York, 1984), 2nd ed. A. G. Shkvarunets et al., IEEE Trans. Plasma Sci. 26, 646 (1998).

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