All ion and electron beams can be characterized by their properties in a 6-dimensional phase space. A parameter called emittance is the area of an ellipse on a plane connecting any two of these six properties. Normally this six-dimensional space is arranged into three two-dimensional planes that roughly correspond to the three coordinates in every day life–horizontal (x), vertical (y), and longitudinal (z).  The parameters plotted on the axes of these planes correspond to 1) horizontal position and angle with respect to the axis, 2) vertical position and angle with respect to the axis, and 3) difference from the average beam energy and phase relative to some reference frequency. Typical low energy beam transport systems don’t use the longitudinal phase space. If the transport system contains no elements that couple horizontal to vertical or longitudinal to transverse variables, the three phase space planes are completely independent and therefore can be analyzed separately.

This situation is most often the case for linear accelerators. The measurement of emittance properties is relatively straightforward. An apparatus for measuring the beam emittance is comprised of a means of slicing out some portion of the beam and measuring the angular content of that beam slice. Scanning this “slicer” through the diameter of the beam produces a measurement of the divergence angles associated with each slice. A plot of these angles as a function of slice position produces an emittance plot.

The emittance characterizes a fundamental property of an ion or electron beam. The smaller the emittance, the better the quality of the beam. Large beam emittances are not only difficult to transport, but are difficult to match into other beamline devices, including accelerator tanks. Brightness is another parameter that is sometimes used to quantify the quality of a beam. Brightness is essentially the beam current divided by the emittance. The reported units of emittance and brightness vary considerably between ion and electron beam systems, so be sure the units are the same when making comparisons of reported values. Ion beam emittances are generally quoted in centimeter-milliradians (cm-mrad) or millimeter-milliradians (mm-mrad) whereas electron emittances are sometimes quoted in meter-radians.

Measurement of the emittance is especially important in low energy beam transport (LEBT) systems. The emittance is a conserved quantity in that it cannot decrease (unless some of the beam is lost or collimated away). Focusing aberrations, radiofrequency acceleration, space-charge forces, etc. all contribute to an increase in emittance. Because all beamline elements have associated acceptances (beam particles outside the acceptance envelope are lost), it is important to know the emittance of the beam at the start of the system. Knowing the emittance enables the focusing elements to be properly tuned to match the beam through the remainder of the accelerator system with minimal emittance growth and/or loss of beam particles.

Low energy emittance scanners come in two basic varieties-slit and collector and the Allison-type scanner developed at LANL (P.W. Allison, J. D. Sherman, and D. B. Holtkamp, IEEE Trans. NS-30 (1983) 2204). The slit and collector scanner utilizes a slit to select a portion of the beam for analysis. The collector is comprised of a series of collector wires to collect the beam particles that pass through the slit. The collector wires are arranged in a series of parallel lines stacked on top of each other parallel to the slit. The beam angle is the arctangent of the distance the collector wire lies above or below the level of the slit divided by the distance between the slit and the collector plane. Alternatively a second slit can be scanned the direction parallel to the first. The beam current passing through the second slit is proportional to the number of beam particles with that particular angle relative to the axis. The two-slit scanner is relatively slow because the second slit has to be scanned through the range for every position of the first slit. The muliwire collector is faster, but requires an amplifier for every wire in the collector.

In contrast, the Allison-type emittance scanner is very quick. The first slit in this scanner selects a portion of the beam just like the slit-and-collector variety. However a second slit is located downstream and fixed along the same line as the first. A pair of high voltage plates is located between these two slits, one above and one below the slits. Changing the voltage on these plates scans the beam passing through the first slit across the second slit. The current through the second slit measures the beam current for the particular angle defined by the voltage on the plates. The voltage on the plates can be changed very quickly, so measurement of the divergence angles in the beam proceeds rapidly.

The beam emittance is derived from a root-mean-square (rms) analysis of the emittance plot. For most beams, the rms ellipse encircles 63% of the beam particles. A 2∙rms ellipse contains 86%, a 4∙rms envelope contains 98% and a 6∙rms ellipse contains 99.8% of the beam particles. Most beam transport simulations utilize 4x, 5x, or 6x emittance ellipses depending on the application. Low energy beam transport systems, where the longitudinal emittance can be neglected, are well-characterized by the 4∙rms emittance ellipse (TRACE2D). Some six-dimensional beam transport simulations utilize the 5∙rms emittance (TRACE3D) whereas others require 6∙rms emittances to properly account for the properties of the beam (PARMTEQ, PARMILA, PARMELA).

SSolutions has designed and fabricated both slit-and-collector and Allison-type emittance scanners. In addition to the hardware, SSolutions has developed an extensive library of emittance analysis and display routines.

Measurement of the emittance of a beam is disruptive in the sense that the measurement disrupts the beam to make the measurement. A non-disruptive technique for measuring emittance was developed to deal with high power beams where the beam energy and/or current is large enough to damage the scanner. This alternative technique is based on tomographic reconstruction of the beam from a number of measured beam profiles. The required beam profiles can be extracted from the light emitted by residual gas atoms in the vacuum system. Hence the tomographic technique does not disrupt the beam to make an emittance measurement.

Tomographic reconstruction is the “T” in medical CAT scanners (computer-aided tomography) and is commonly used to reconstruct two-dimensional images from a series of one-dimensional x-ray profiles in medical imaging. Similarly, tomographic reconstruction can be used to reconstruct beam emittances from a series of beam profile measurements. The early reconstruction algorithms required several minutes to reconstruct a beam profile. However advances computer power enable reconstruction of the beam emittance in real-time. This approach is a very powerful because it displays the exact information that an operator needs to tune the beam without disrupting it.