Cooling system

The cooling module for the vacuum chamber is the LN2 trap design from IdealVac. The specs for this module can be found [here].

We have the sample cooling plate from IdealVac, which has a 140ml LN2 reservoir. To fill the reservoir, asked for a quote for https://www.linde-cryo.nl/nl/producten/cryopro/dermatologische-behandeling.html - this is no longer a viable option for the setup.

First equations for LN2 required to cool

The first planned measurement is the fluorescence measurements. For these, we will use the three-faced sample holder hung from the roof of the chamber. This design is given as a thumbnail. We should also know how much LN2 is required to cool this to 173K (operating temperature). In order to calculate this, we need to know several thermal properties of the holder. This holder will be made of copper which has well-known values for heat capacity and density. The amount of heat required to achieve this from room temperature can be calculated via the equation

   Q=VCp(T2-T1)

where Q is the heat energy required, V is the volume of copper used, C is the heat capacity of copper, p is the density of copper and T2-T1 is the temperature difference required. Using the standard values, C=0.389kJ/kgK and p=8940kg/m^3, the sample holder with a volume of 3.3e-4m^3 will require **115kJ** of heat energy. This heat energy will be supplied by the vaporisation of liquid nitrogen in the LN2 cooling module. This is given as 199kJ/kg with a mass as 0.8083kg per liter. Therefore, for the 140ml cooling module, the cooling system of the setup will provide **22.798kJ** per fill. This means the module should be refilled **5 times** to cool the sample holder only to 173K. Since each refill takes maximum 2 hours to evaporate (as measured under vacuum with no warm components attached to it), this is a **10-hour** procedure (of course, this will reduce when the warm elements are introduced to the system and we need not wait for all LN2 to evaporate entirely before refilling, provided we are careful of bubbling).

This same calculation for three copper cables connected to the reservoir will require **37.18kJ**, corresponding to **1-1.5** reservoir fills. In total, this sums to a maximum of **6.5** reservoir fills taking roughly **13 hours** and 1L of LN2.

Extra considerations:

• Heat loss to radiation
• Poor thermal connections
• Time taken for reservoir to evaporate when pieces are connected
• Heat loss to frame
• Temperature difference at each end of the copper braids

Copper cables

The LN2 trap will be connected to the sample holder via one copper thermal cable per sample-space. For example, the sample holder built by Casimir for reflective measurements has space for two samples and will therefore be connected to two thermal cables. These thermal cables are ordered from Technology Applications, Inc. The dimensions of which were chosen to fit within the chamber without interfering with the walls or other components, and with enough slack to twist up to 180 degrees to accommodate the movement of the sample holder. <add simulation information> The designs are given below.

Figure 1: Thermal strap design

This design is based on a standard design (P6-504) from the company to reduce shipping time and increase modularity of use with both sample holders, which can be found here File:2022 CuTS® Catalog - TAI(1139).pdf. This strap is made of 9 individual copper braids with a length of 20cm and width of 2.54cm, connected to two L-shaped end pieces. Some broad thermal information is provided from the company and shown below.

Conductance (W/K)

	50mm	100mm	200mm
300K	0.18	0.10	0.05
77k	0.26	0.14	0.07
40K	0.52	0.31	0.17
10K	0.42	0.24	0.14
4K	0.16	0.09	0.04

Equipment

Small dewars are widely available for LN2 handling and transportation. These come in many different sizes but based on the small 140 ml LN2 reservoir, we shouldn't need anything above 1 l to store LN2 intended for cooling the plate. Transfer out of the dewar can take place with several options, such as pouring through a spout and into a funnel or scooping small amounts out at a time. While pouring is a viable option since some dewars do come with a spout in place, scooping LN2 in a pre-determined-sized cryo dipper is a more careful and predictable way. This method can also use a simple funnel to prevent over spilling, though it should be considered also in the context of evapouration of the LN2 out of the LN2 trap, which could cause bubbling and splash on the sample chamber. Covering the chamber can prevent any accidental splashing.

From the module specs, we know that the LN2 reservoir can hold 140ml at a time. To cool this to liquid nitrogen temperatures (-196 degrees) requires 1L of LN2. From that point forwards, each 140ml of LN2 will take a maximum of 2 hours to evaporate out of the reservoir. This can of course be topped up at any convenient time to extend this time. With this in mind, we should look to get a dewar of 2L (or 3L for some extra wiggle room) to prevent needing to refill it. The dipper we use should also be capable of holding 200ml of LN2 in order to fill the reservoir in one pour, ideally with a spout to facilitate ease of movement.

Caption text

Product	Price	Link
2L Dewar	€216.00	[Dewar]
3L Dewar	€137.99	[Dewar]
200ml ladle	€19.95	[Dipper]