Description

Fig. 4.6 shows a diagram of the chosen vacuum scheme. The system is composed of 6 different vacuum chambers connected by small apertures.

The values of the most relevant parameters shown in Fig. 4.6 and used in the experimental setup which will be useful in the following discussion are listed in table 4.1 for each chamber.

Chamber # Skimmer coord. [mm] Skimmer Dimen- sions [mm] Subtended Solid angle [sr] Chamber Volume [l] Pumping Speed [l/s] 1 5 ø 0.17 9.1·10−4 2.2 277 2 25 ø 0.4 2.0·10−4 4.0 277 3 325 4 x 0.4 1.5·10−5 _{1.5 76} 4 800 ø 15 2.8·10−4 30.6 678 5 1010 ø 15 1.7·10−4 1.9 76 6 −− −− −− 1.0 277

Table 4.1: Quantities relevant to vacuum calculations for each chamber.

4.2 Vacuum system

Figure 4.6: Schematic representation of the vacuum scheme used in the beam profile monitor test stand, including aperture identification numbersaj.

the interaction chamber, there is no need for a large suction power, as no major gas load is expected. Rather, compression ratio becomes an issue to keep the vacuum low against the constant out-gassing of the elements present inside the chamber (detectors, electron gun, movable parts etc.). In the case of the nozzle chamber, instead, the main issue is the ability to dump efficiently the gas load given by the gas jet. The reason for using two different channels of pre-vacuum pumps is to avoid backflow to the dumping and interaction chamber when the jet is turned on and the gas load on the nozzle and skimmer chamber increases drastically.

Given the vacuum to be reached (10−8 to 10−9 mbar) in the first stages of the experiment, oil-free pumps are essential, and cryopumps are not needed, as almost all commercial TMP can provide a 10−9 mbar vacuum. As shown in Fig. 4.6, 9 pumps are employed, 6 TMPs and 3 pre-vacuum pumps (nominal pumping speed reported in the following):

• 1 large TMP (700 l/s) for the interaction chamber on a DN160 flange.

• 2 small TMP (80 l/s) for the first stage of the dumping chamber and for the differential pumping section on a DN70 flange.

• 3 medium TMP (300 l/s) for the remaining chambers, on a DN100 flange.

• 3 Scroll pumps (1 x 30 m3/h, 2 x 15 m3/h) for pre-vacuum.

4.2.2 Nozzle chamber

To describe the behavior of pressure in the nozzle chamber the mass flow through the nozzle and the pumping speed need to be taken into account. The mass flow through the nozzle ˙mnozzle can be estimated by (2.15). It depends only on orifice geometry,

pre-pressure and gas species and is therefore constant in time. On the other hand the mass flow through the TMP depends on the actual pressure in the chamber Pa, and

the pumping speed of the pump, which is also a function ofPa. The dependence of the

pumping speed fromPa comes from the power limitations of the pump, which increase

as the volume swept (proportional to the pumping speed) is filled by more and more gas as the pressure increases, and is given by the manufacturer. The plot in Fig. 4.7 refers to the pumping speed of the TURBOVAC SL300, the 300 l/s TMP (nominal

4.2 Vacuum system

pumping speed) installed in the nozzle chamber, and is provided by Oerlikon Leybold.

Figure 4.7: Pumping speed in terms of vacuum chamber pressure for the SL300 TUR- BOVAC TMP from Oerlikon Leybold. The pumping speed curve forN2 is approximated

by an exponential relation expressed by (4.1).

The pumping speed can be approximated with an exponential, and in particular the curve for the pumping speed forN2 can be expressed by (4.1):

S[l/s] = 277e−10.2Pa[mbar] (4.1) Therefore, the mass flow through the pump can be expressed as the product of the mass per liter of gas at the thermodynamic conditions of the ambient chamber times the pumping speed:

˙ mpump = nW V ·S = PaW RTa ·0.277e−0.102Pa _(4.2)

where the pumping speed is expressed in m3/s rather than in l/s for unit coherency and Pa in Pascal. The equilibrium condition will be obtained when ˙mpump = ˙mnozzle,

and will correspond to an equilibrium pressure, indicated withPa−e, which is in turn a

function of the pre-pressureP0 and the nozzle diameterd. This calculation ignores the gas mass which escapes the chamber through the skimmer. However, as it was shown in Chp. 2, this mass is less than twice the mass that would escape from the nozzle

in case of an effusive source: thus its ratio to the contained mass is less than twice the solid angle spanned by the skimmer over the full 2π solid angle. For a skimmer aperture of diameter 180µm at 5 mm distance from the nozzle, this equates to about 0.03%: such low value is negligible in the following calculation. When (4.2) is equated to (2.15) calculated for the nozzle orifice, a transcendental equation is obtained, which can only be solved numerically. Fig. 4.8 shows a plot of the two mass flows, through the pump and through the orifice, calculated for a 30 µm orifice diameter, at 10 bar pre-pressure, with the SL300 TURBOVAC TMP from Leybold.

Figure 4.8: Calculated mass flow through the pump and through a 30 µm diameter orifice, at room temperature and 10 bar pre-pressure, with the SL300 TURBOVAC from Leybold, forN2 gas.

It is possible to identify in Fig. 4.8 two points of equilibrium, in which the two mass flows are equal. However, only the first of such points, the one for lower pressures, is a stable equilibrium point. Indeed, when the mass flow through the pump is smaller than the mass flow from the orifice, the pressure in the chamber rises, so the system moves rightward in the plot, and vice versa. Therefore, any displacement from the equilibrium position pushes the system towards equilibrium for a positive slope of the pumping mass flow and away from equilibrium for a negative slope of the pumping mass flow.

4.2 Vacuum system

which will be reached in the vacuum chamber: something which can be easily measured to provide experimental validation of the theory here described. This experiment was carried out with two different TMP with different pumping speed curves. Fig. 4.9 shows a plot of the calculated equilibrium pressuresPa−e for both pumps and different

values of pre-pressureP0, together with the measured data.

Figure 4.9: Equilibrium pressure Pa−e in the nozzle chamber for two different TMP

(300 and 180 l/s nominal pumping speed) and for different values of the pre-pressure P0.

Calculations are done for a 30µm diameter circular orifice at room temperature, with N2

gas. The continuous line represents the calculation while the points are experimental data. The error bars are quoted from the datasheet specifications of the pressure gauges.

The measured data is in very good agreement with the calculations. To reach this agreement, the nominal pumping speed of the TMP, as derived from the pumping speed curve on the datasheet, was decreased to optimize the agreement with the experimen- tal data, so as to take into account the convoluted geometry of the chamber, which inevitably results in decreased pumping efficiency. That the pumping speeds are only slightly smaller than the ones reported in the manufacturer data is testament to the good design of the chamber, as well as providing an indication of the theory validity. Finally, the mass flow rate can also be expressed in terms of the pressure rate of change:

˙

m = ˙nW = ˙Pa

VchamberW

RTa

Therefore if ˙m in (4.3) is substituted with the net mass flow rate, given by ˙mnet =

˙

mnozzle−m˙pump, eqn. (4.2) can be expressed as a differential equation in terms of Pa

and its derivative: ˙ Pa = ˙ mnozzle− PaW RTa 0.277e−0.102Pa RTa VchamberW (4.4) This differential equation can be solved numerically, and provides the time evolution of the system. The relatively simple form of (4.4) comes from the fact that ˙mnozzle

does not depend on Pa. However, (4.4) also assumes that any mass inflow through

the nozzle would be immediately transported to the pump inlet. A rough estimate of how long it takes for the mass entered at the nozzle orifice to reach the vacuum pump is of the order of milliseconds (see section D.5). This can be taken into account in (4.4) by introducing a time delay ∆t between the establishment of the pressure in the chamber, calculated in (4.3), and the pressure seen by the vacuum pump, relevant to the pumping speed and appearing in (4.4):

˙ Pa(t) = ˙ mnozzle− Pa(t−∆t)W RTa 0.277e−0.102Pa(t−∆t) RTa VchamberW (4.5) When (4.5) is solved for varying values of ∆t, the transient of the pressure in the chamber can be obtained, giving an estimate of the time needed to reach equilibrium; This is done in Fig. 4.10. Analysis of Fig. 4.10 shows that the rise time, defined as the time needed by the system to reach 90% of the final pressure, is of the order of 20 ns for delays up to a few ms, decreasing down to 10 ms for higher delays. However, the rise time also presents a strong dependence on the effective pumping speed of the TMP, as shown in Fig. 4.11.

Such decrease in pumping speed can come from different factors: geometrically, the aperture where the pump is mounted limits the pumping speed, while mechanically, overheating of the pump causes the rotation speed to decrease as a built-in protection to the bearings and the motor.