UC Davis PDG: Reflectometry
Profile Plasmas are dispersive media whose refractive index is a function of plasma density; higher frequency radiation reflects from higher density plasma layers. Reflectometry, as its name suggests, exploits the reflection of electromagnetic waves from plasma cut-offs to either measure density profiles or spatially resolve density fluctuations:

- polarized parallel (O-mode) to an external magnetic field, the reflectometer signal reflects from the plasma cutoff layer fp.
- polarized perpendicular (X-mode) to an external magnetic field, the signal reflects from the right-hand cutoff layer fR.

Shown to the right is a characteristic frequency plot for the TEXTOR-94 tokamak in Germany. Here, the O-mode frequency range is DC-50 GHz, while the X-mode frequency range is 50-90 GHz.

Reflectometry techniques basically fall into two categories. The first are phase measurement techniques in which the phase of the reflected wave is measured with respect to the probing wave. The second are time-of-flight measurement techniques in which the time required for the probing wave to propagate to the cutoff layer, reflect and then propagate back out of the plasma is measured. Although phase measurement techniques are more commonly employed, significant advantages may be realized with time-of-flight techniques when applied to high density, high field fusion plasmas.

The UCD Plasma Diagnostics Group is researching various aspects of reflectometry for plasma density measurements in current plasma devices as well as next generation devices such as ITER. Theoretical, computational, basic experimental and technological development efforts comprise a concerted research program designed to elucidate the physics of fluctuation reflectometry and produce innovative instruments.

Density Profile Diagnostic Systems
Both phase measurement and time-of-flight measurement techniques may be applied to plasma profiles. For O-mode operation, in which the cutoff frequency is solely a function of electron density, the group delay data (in the case of time-of-flight techniques) or a derivative of the phase delay data (in the case of phase measurement techniques) may be Abel-inverted to reconstruct the electron density profile of the target plasma. The most common approach is a phase measurement technique called swept frequency modulation (FM) reflectometry, while two different time-of-flight techniques have been applied to this problem: amplitude modulation (AM) reflectometry and ultrashort pulse reflectometry (USPR). Discussion of the advantages and disadvantages of each of these methods follows.

FM Reflectometry
FM reflectometry systems utilize one or more swept frequency sources to cover the frequency range of interest. Mixing a portion of the transmitted radiation with that reflected from the plasma produces an IF signal whose frequency is proportional to the double-pass phase delay. The presence of large density fluctuations, however, create spurious phase changes that are difficult to separate out from the multifringe phase changes formed by the reflectometer. The solution in most cases is to dramatically decrease the sweep time of the FM source so as to “freeze” the fluctuations in place during a single sweep. In the past, slowly swept BWOs have been utilized with sweep times of 0.1-1.0 ms. More recently, a new generation of fast-swept millimeter-wave sources have been employed which combine fast-swept solid-state microwave oscillators with broadband frequency multipliers, thereby achieving sweep times as short as 0.02 ms.

The swept-FM technique measures the phase delay of the electromagnetic wave, while USPR measures the group delay. For O-mode reflectometry, the density profile can be easily reconstructed using an Abel inversion of recorded USPR group delays. For the swept-FM systems, the derivative of the phase delay information is required which can add a considerable amount .

Unfortunately, the extremely short sweep times translate into high digitization rates (10-50 MSample/sec on DIII-D, for example). This results in extremely high data loads, and considerable demands placed on numerical post-processing to extract the requisite phase information from the raw data. As the d(Phase)/d(Frequency) is required for Abel-inversion, this can add a considerable amount of “numerical noise” to the data (alternatively, the phase delay data can be heavily filtered). In addition, a chain of inefficient multipliers is required to achieve the high frequencies required on high performance plasma devices, resulting in increased complexity and a considerable decrease in the amount of millimeter-wave power transmitted into the plasma.

Ultrashort Pulse Reflectometry (USPR)
Time-of-flight radar systems function by reflecting short pulses of electromagnetic radiation. By collecting double-pass time delay data at many distinct frequencies, it is then possible to invert the time delay data to generate plasma density profiles. Moderate pulse reflectometry is a time-of-flight radar technique which propagates a short duration pulse of microwave or millimeter-wave radiation with a relatively well defined frequency. Complete density profile data are obtained by either sweeping the frequency of the pulsed millimeter-wave source, or by using a series of distinct frequency sources. Ultrashort pulse reflectometry or USPR is similar to moderate pulse reflectometry, except that an extremely short pulse (or high speed chirped waveform) containing frequency components that span the desired plasma density profile. With USPR, reflection data at multiple frequencies may be collected simultaneously with a single pulse or high speed chirp.

The UC Davis Plasma Diagnostics Group is actively investigating the USPR technique, and applying it to a number of fusion plasma devices both in the U.S. and abroad. Data collected on the Sustained Spheromak Experiment (SSPX) device are now routinely collected and utilized to generate time-resolved density profiles of SSPX plasmas.

In addition, technological advances in state-of-the-art high speed millimeter-wave switches (for moderate pulse reflectometry) and nonlinear transmission lines (for USPR) are also under development by the Millimeter Wave Technology Group at UC Davis.

AM Reflectometry
AM reflectometry involves the amplitude modulation of the probing reflectometer beam. The phase of the modulated millimeter-wave envolope may be easily measured, and provides a group delay measurement similar to the moderate pulse reflectometry and USPR techniques. Its biggest disadvantage is the near impossibility of distinguising between false and real reflections. Extreme care must therefore be taken to eliminate false reflections from entering the detector/mixer before the system can produce significant, believable profiles.

The high speed millimeter-wave switching technology required to implement AM reflectometry on next generation tokamaks such as ITER, however, is identical to that required for moderate pulse reflectometry and is under development by the Millimeter Wave Technology Group at UC Davis.

Density Fluctuation Diagnostic Systems
In addition to determining electron density profiles, reflectometry is known to be extraordinarily sensitive to density fluctuations. To conduct electron density fluctuation measurements, the frequency of the probing reflectometer beam is kept constant (rather than being swept or modulated), so that small density fluctuations near the reflecting layer can both phase and amplitude modulate the probing beam. The actual mechanism by which fluctuations modulate the reflected beam, however, and issues of localization and wavenumber sensitivity, remain poorly understood. The UCD Plasma Diagnostics Group is therefore conducting a multifront approach to investigate the physics of reflectometry, utilizing theoretical and computational modelling as well as an innovative effort to visualize density fluctuations via Microwave Imaging Reflectometry in which reflections from a large area of the plasma cutoff surface are imaged onto a detector array.

CW reflectometry, in which a constant frequency source is utilized to probe the plasma, is by far the commonly applied and most fluctuation sensitive of all the forms of reflectometry. It is limited, however, to monitoring density fluctuations on only one cutoff layer per probing frequency.
 

email  Comments to: Calvin Domier