Time-of-flight radar systems function by reflecting short pulses of electromagnetic radiation from a target medium. The double-pass time delay from transmitter to receiver is then used to compute the distance to the reflecting medium. Plasmas are dispersive media whose refractive index is a function of plasma density; higher frequency radiation reflects from higher density plasma layers. In the case of plasmas, whose refractive index is a function of electron density, collecting double-pass time delay data at many distinct frequencies (thereby reflecting off many distinct density layers) permits the time delay data to be inverted to generate electron density profiles.

In a conventional moderate pulse reflectometry system, a wavepacket with a well defined frequency (i.e. narrow spectral width) and moderate time duration (~ 1 nsec) propagates into the plasma from a transmitting horn, reflects, and finally returns to be collected by a receiving horn.By sequentially switching a number of distinct frequency microwave or millimeter-wave sources and performing double-pass time-of-flight measurements of each of the reflected wavepackets, the distance to each reflecting layer is obtained allowing the electron density profile to be computed.The high cost associated with implementing a multichannel MPR system with sufficient frequency resolution (i.e. number of channels) to obtain accurate density profiles has, however, limited the implementation to a 4 channel system on the RTP tokamak which has been recently upgraded to 10 channels for use on the TEXTOR tokamak.

Ultrashort-pulse reflectometry (USPR) significantly reduces the hardware complexity of the MPR system by replacing the series of sequentially switched sources with a single ultrashort-pulse source or chirped waveform which contains frequency components spanning the desired plasma density profile (or a significant fraction thereof). Each frequency component of the incident wavepacket reflects from a different spatial location (density) in the plasma. By separating different frequency components of the reflected wavepacket and obtaining time-of-flight measurements for each component, the density profile can be determined with just one source and a single set of measurements.


As stated previously, USPR involves the propagation of an ultrashort pulse or chirped waveform which contains frequency components spanning the desired plasma density profile. Upon reflection, each component in the incident wave packet reflects from a different spatial location (density layer) in the plasma, thus spreading out the reflected wave packet in time. The reflected wave packet is amplified and passed through a multichannel filter bank. Ultrafast Schottky diode detectors convert each of the filtered microwave wave packets into RF pulses whose double-pass time delay is then measured. In the original USPR concept, extremely short impulse sources were envisaged. Significant advantages have been realized through the replacement of the impulse source with a chirped waveform whose frequency monotonically increases or decreases in time and whose duration is sufficiently short that the frequency components of each USPR channel (occupying a bandwidth df) occur over a period of time t << 1/df. By dispersing the energy contained in a conventional ultrashort pulse into a chirped waveform, its peak power can be significantly lowered without reducing the total energy contained within the pulse. Low cost microwave amplifiers can then be used to significantly increase the energy of the transmitted pulse by 20 dB or more. For an extremely broadband USPR system, wideband balanced mixers may be utilized to upconvert the low frequency chirp to millimeter-wave frequencies. Using highpass waveguide filters to ensure single sideband operation, each mixer is then capable of covering a portion of the IF frequency space. By coupling this chirp signal to a series of millimeter-wave mixers, and utilizing a multithrow IF switch to successively connect the reflected waveform to an IF system, extremely broad frequency coverage may be obtained at relatively low cost. After downconversion by the mixer, the reflected wavepacket is amplified and passed through a multichannel filter bank. Ultrafast Schottky diode detectors convert each of the filtered microwave wave packets into 1-3 nsec duration pulses. Time delay measurements on the post-detection pulses, each representing a different probing reflectometry frequency, are performed in a manner similar to that in moderate pulse reflectometry. Numerous methods exist to measure the time interval between a start and stop pulse. First, the variable amplitude detector pulse must be converted into a constant amplitude pulse using a timing discriminator such as a leading-edge disriminator or a constant fraction discriminator (CFD). CFDs are preferred in this application where the input signals have a wide range of amplitudes but a relatively constant pulse shape, since they trigger at a constant fraction of the pulse amplitude. This makes CFDs relatively insensitive to amplitude fluctuations. The CFDs are followed by time-to-amplitude converters (TACs), which convert double-pass USPR time delay data into analog voltages which are subsequently digitized.

A more elegant, although technologically more challenging, approach to extending USPR to higher frequencies lies in the direct generation of high power ultrashort pulses or millimeter-wave chirp signals. Nonlinear transmission lines (NLTLs) have great promise as impulse and shock line generators. NLTLs have already been reported in the literature which produce ~5 psec FWHM pulses with peak output powers of ~1 W, which would be sufficient for use on devices such as the DIII-D tokamak. In addition, other approaches are under investigation for the generation of ultrashort pulses of even larger amplitude.


The first multichannel USPR system was designed and fabricated by the UC Davis Plasma Diagnostics Group, and successfully tested on the CCT tokamak at UCLA in 1994. CCT Experimental results show good agreement with both theory and with other CCT diagnostics. This first 7 channel system, however, was limited to a single profile measurement per plasma discharge. An improved 8 channel USPR system has since been developed, which is capable of acquiring high resolution (25 psec corresponding to < 4 mm spatial resolution) multichannel time delay data at high repetition rates (> 100 kHz).

By using the upconverting mixer approach, an extremely broadband O-mode USPR system has been developed for the measurements of the electron density profiles and fluctuations on the Sustained Spheromak Physics Experiment (SSPX), which was developed at LLNL to be used in further exploring the physics of the spheromak fusion concept. The USPR input source is a state-of-the-art commercially available impulse generator (Model : Picosecond Pulse Labs 3500c).It is a 5 V, 65 psec duration (FWHM) source. In the USPR system for SSPX, as mentioned earlier, broadband millimeter-wave mixers are utilized to upconvert the radiation to higher frequencies; however, these mixers are limited to IF signals that are 500 mV.It is therefore necessary to disperse the impulse signal into a monotonically increasing frequency chirp (using short lengths of dispersive waveguide sections) and thereby spread out its energy in time.This chirp permits low cost microwave amplifiers to increase the energy of the transmitted waveform.Since the power spectrum falls off dramatically above ~8 GHz, most of the power resides in the lower frequencies (<9 GHz).This results in relatively poor signal-to-noise (S/N) IF signals above 9 GHz.In order to increase the power of the high frequency (>10 GHz) components, the resultant chirp is divided into three portions, with one portion providing a low frequency chirp (6-10 GHz), another portion propagated through a length of WR-62 waveguide (cutoff=9.49 GHz) to yield 11-15 GHz, and the last portion through a length of WR-42 waveguide (cutoff=14.08 GHz) to yield 16-19 GHz. In addition, a passive frequency doubler (MITEQ, MX2M060260A) is employed to further increase the power levels at the higher frequencies. In the SSPX USPR millimeter-wave subsystem, six millimeter-wave mixers are utilized to convert the USPR frequencies from the IF frequency range of 6-18 GHz to the plasma (RF) frequency range of 33-158 GHz and vice versa.Up-converted millimeter-wave chirp signals are launched into the plasma via the waveguide and horn assembly.Reflected plasma signals are propagated back to the millimeter-wave mixers via the same waveguide path the transmitted signals enter. The USPR receiver subsystem is designed to take the down-converted output from the USPR millimeter-wave subsystem and break it down into eight filtered, detected pulsed waveforms spanning a frequency range of 6 to 18 GHz.Outputs from this subsystem consist of eight filtered analog detector signals.The amplitude of each detector signal is proportional to the time delay experienced by the corresponding channel.

The SSPX USPR system is capable of routinely generating reconstructed density profiles as a function of shot number and discharge time. When raw USPR data are decoded and reliable time delay data are obtained for each channel, electron density profiles are ready to be reconstructed by an IDL routine. Generally, the USPR profiles show good agreement with the Thomson scattering profiles in the outer plasma regions, i.e. up to near the magnetic axis, as long as the Thomson scattering data shows monotonically increasing profiles to that point.It should be stressed here that the USPR density profiles are a direct result of Abel inversion of the raw time delay data with no fitting or smoothing technique other than a simple averaging over a 57 ms time window.

For more information, contact Dr. Calvin Domier at cwdomier@ucdavis.edu.