# Presentation: 233804

## Lonny Berman EFAC May 10th  2007

- ID Beamline Optics and Damping Wigglers

## Outline

- Hard x-ray undulator beamline monochromator thermal modelling (silicon and diamond)
- Hard x-ray undulator beamline mirror modelling
- Damping wiggler beamline monochromator thermal modelling (silicon)
- Damping wigglers:  to cant or not to cant

## Undulator Beamline Silicon Monochromator

- Simulation of “hockey-puck” liquid nitrogen cooled crystal design using 2σ beam size (1.2 mm wide x 0.75 mm high) from U14 superconducting undulator at maximum K, 30 m distance from source, 12.7o Bragg angle (corresponds to 8.9 keV for Si(111)).
- Total power = 109 W (unfiltered), 92 W (filtered)
- Maximum temperature = 98 K (unfiltered), 94 K (filtered)
- Maximum thermal slope error in beam footprint = ±5 μrad (unfiltered), ±4 μrad (filtered)

- Courtesy of Viswanath Ravindranath

## Performance for Longer Undulators

| U14 Undulator Length (m) | Filtered or Unfiltered | Total Power at Maximum K | Maximum Temperature (K) | Maximum Thermal Slope Error (μrad) |
| --- | --- | --- | --- | --- |
|      2 | unfiltered |    109 |     98 |    ±5 |
|      2 |   filtered |      92 |     94 |    ±4 |
|      4 | unfiltered |    219 |    144 |  ±7.4 |
|      4 |   filtered |    185 |    125 |    ±1 |
|      6 | unfiltered |    326 |    232 |  ±100 |
|      6 |   filtered |    275 |    180 |   ±32 |

## 4 m Long Undulator Case with Filter

**Conclusion:**  for silicon, there is no better temperature for the illuminated area of the crystal to be at, than 125 K.
**Action Item:**  investigate the use of controls and diagnostics to make sure that this is the temperature of the illuminated area of the crystal.

## Using a Water-Cooled Diamond

- The diamond wafer is 0.5 mm thick and the (111) Bragg reflection is used (Bragg angle is 19.7o at 8.9 keV).  Beam size 2.4 mm wide x 1.5 mm high (4σ).
- Here, 60% of the incident power is transmitted through the crystal, and the depth dependence of the 40% absorbed power has to be taken into consideration.  The transmitted power propagates through a hole in the copper substrate.  There is 1 mm of overlap of the diamond wafer and copper substrate all around.  A crucial consideration, in such a design, is the thermal contact between the diamond and the substrate.

- Courtesy of Paul Montanez

## Diamond Crystal Peformance

| Means of Thermal Contact of Diamond with Copper (Presumed Heat Transfer Coefficient in W/mm2-°C) | Power Absorbed by Diamond (W) | Maximum Temperature of Diamond (°C) | Maximum Thermal Slope Error (μrad) |
| --- | --- | --- | --- |
| Ga-In Eutectic (0.04) |     166 |     267 |    ±30 |
| Brazing (0.4) |     166 |     103 |      ±9 |

**Conclusion:**  pathways to improvement involve better thermal contact, larger contact area, thinner diamond to absorb less power.
**Action Item:**  watch developments in the field, as the main challenge with diamonds is in obtaining an assured supply of large, good quality crystals.

## NSLS X25 1 m Long Vertical Focusing Mirror

**X25 Vertical Mirror Parameters**
- Source to Optic = 23 m
- Optic to Focus = 3.5 m
- Demag = 6.6:1
- measured rms slope = 1.4 μrad
_**NSLS-I**_
- perfect image size *fwhm *= 3.25 μm
- calc. image size incl. fig. err. *fwhm* = 23 μm
_**NSLS-II**_
- perfect image size *fwhm *= 1.1 μm
- calc. image size incl. fig. err. *fwhm *= 23 μm

**1 m long dynamically bent palladium coated mirror, fused silica substrate.**

- 23 m

- 3.5 m

- X25 Mirror Bender System

- Courtesy of James Ablett

## X25 SHADOW Ray-Tracing

- Ideal Mirror

- X25 Mirror

- Source

- X25 Mirror, ‘width’ ~ 16 μm Ideal Mirror, fwhm = 1.03 μm

- x [mm]

- Normalized Intensity

- X25 Mirror at NSLS-II

- Source

- Ideal Mirror

- X25 Mirror

- X25 Mirror, fwhm = 16.6 μm Ideal Mirror, fwhm = 3.2 μm

- y [μm]

**X25 Mirror at NSLS-II**

- x [mm]

- Normalized Intensity

- y [μm]

- rms slope=1.4 μrad

- distance along mirror [cm]

- vertical [microns]

- vertical [microns]

**X25 Mirror at NSLS-I**

- distance along mirror [cm]

## Damping Wiggler Silicon Monochromator

- We looked at the same crystal design as we used for undulator beams, and studied its performance using different size wiggler beams.
- The case shown here is based on a beam size of 3.6 mm wide x 2.25 mm high at 30 m from the 7 m long damping wiggler source (original design), Si(111) at 8.9 keV (Bragg angle 12.7o).
- Total power = 475 W
- Maximum temperature = 125 K
- Maximum thermal slope error in beam footprint = ±6.6 μrad, not bad!

- Courtesy of Viswanath Ravindranath

## Damping Wiggler Mono Using Bigger Beam

- We also looked at the case of a beam size twice as large in the horizontal and vertical directions, i.e. 7.2 mm wide x 4.5 mm high.
- Total power = 1.77 kW
- Maximum temperature = 355 K
- Maximum thermal slope error in beam footprint = ±300 μrad
- Notice that the temperature rise in this case is no longer concentrated right at the beam footprint.  The crystal is too small in size to handle the power.
**Conclusion:**  bigger beams require bigger crystals with bigger cooling interfaces.

- Courtesy of Viswanath Ravindranath

## Damping Wigglers:  To Cant or Not to Cant

- Multiple yet independent damping wiggler beamlines may be accommodated in individual straight sections, either by viewing different off-axis portions of the same damping wiggler fan, or by viewing on-axis radiation emissions from separate wigglers which are canted by a few milliradians with respect to each other.
- The larger the canting angle, the larger the impact on the emittance of the ring.  E.g. if two 3.5 m long wigglers canted by 2 mrad with respect to each other are installed in each of these 8 straight sections, then the emittance increases by 8%.

- 2 mrad

- Critical Energy Dependence Across Each Canted Wiggler Radiation Fan

- For each fan:
- Ec = Ec,max(1-[ө/өmax]2)1/2
- өmax = K/γ

- 10.8 keV

- Ec (keV)

- ө (mrad)

- 10

- 5

- 0

- 0

- 5

- -5

## Flux Variation Across Wiggler Fan

**Flux Conclusion:**  canted damping wigglers offer no advantages for flux-dependent applications except at the highest photon energies, as compared with viewing the fan at even 1.5 mrad off-axis horizontally.

- Courtesy of Steve Hulbert

## Brightness is a Different Matter

- Insertion device codes do not handle this effect correctly, but it has been empirically observed at the X25 wiggler:

- Lonny Berman and Zhijian Yin (1997)

**Brightness Conclusion:**  when viewed at 1 mrad off-axis horizontally, the horizontal source size of a 7 m long damping wiggler will appear to be 7 mm wide, diminishing the brightness _by a factor of ~20_, relative to on-axis viewing.

- If brightness is an important consideration for a damping wiggler source, it must be viewed on-axis.  The only means to achieve this, for two completely independent beamlines, is to implement canted damping wigglers.

## Conclusions

- Existing liquid nitrogen cooled silicon crystal design will handle NSLS-II undulator beams, with attention to temperature control
- For water-cooled diamond crystals to be effective in NSLS-II undulator beams, attention to crystal size and thermal contact is necessary
- Small mirror figure errors can introduce structure into an NSLS-II undulator focused beam as well as blur image
- Liquid nitrogen cooled silicon crystal designed for an NSLS-II undulator beam could handle a damping wiggler beam with dimensions of ~4-5 mm; larger size beams will need to be handled by larger size crystals
- Canted damping wigglers pose no advantage for flux-dependent applications (compared with off-axis views of a single wiggler), but will be necessary for brightness-dependent applications if more than one independent beamline per damping wiggler straight section is desired