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ATS/Note/2012/043 TECH 2012-05-09 [email protected] Vacuum simulation of the LINAC4 H - source Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP Keywords: electrical network vacuum analogy, dynamic vacuum, LINAC4 H- Source, Monte Carlo, pressure profile, hydrogen, LIU Summary The 160 MeV H - Linac4 will replace the 50 MeV proton Linac2. Linac4 H - source is the new ion source. In order to study its dynamic behaviour from the vacuum point of view, the electrical network – vacuum analogy have been used. This technique allows the evaluation of the hydrogen partial pressure profile as a function of time and position, giving important information about plasma chamber and LEBT pressures. Aiming at benchmarking the following simulations, several experimental calibration campaigns are foreseen in the near future: the H - source of Linac4 requires a pulsed injection of hydrogen to reach the typically 0.1 mbar pressure mandatory for plasma formation. First preliminary results show good agreement between the experimental and the simulated profiles. 1. Linac4 H- source Aiming at improving LHC intensity and luminosity and in order to replace LINAC2, dating 1978, the upgrade of the whole injector line is foreseen to take place within the next years: in this framework LINAC4 has been designed. Linac4 is composed of an ion source, a Low Energy Beam Transfer (LEBT), a Radio Frequency Quadrupole (RFQ) and a chopper line, an Alvarez Drift Tube Linac (DTL), a Cell- Coupled Drift Tube Linac (CCDTL) and a Pi-mode structure (PIMS) [ref 1] (see Fig. 1). This note concerns the vacuum system from the H - ion source to the RFQ.

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Page 1: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

ATS/Note/2012/043 TECH

2012-05-09

[email protected]

Vacuum simulation of the LINAC4 H- source

Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP

Keywords: electrical network vacuum analogy, dynamic vacuum, LINAC4 H- Source, Monte Carlo, pressure profile, hydrogen, LIU

Summary The 160 MeV H- Linac4 will replace the 50 MeV proton Linac2. Linac4 H- source is the new ion source. In order to study its dynamic behaviour from the vacuum point of view, the electrical network – vacuum analogy have been used. This technique allows the evaluation of the hydrogen partial pressure profile as a function of time and position, giving important information about plasma chamber and LEBT pressures. Aiming at benchmarking the following simulations, several experimental calibration campaigns are foreseen in the near future: the H- source of Linac4 requires a pulsed injection of hydrogen to reach the typically 0.1 mbar pressure mandatory for plasma formation. First preliminary results show good agreement between the experimental and the simulated profiles.

1. Linac4 H- source

Aiming at improving LHC intensity and luminosity and in order to replace LINAC2,

dating 1978, the upgrade of the whole injector line is foreseen to take place within the next years: in this framework LINAC4 has been designed.

Linac4 is composed of an ion source, a Low Energy Beam Transfer (LEBT), a Radio Frequency Quadrupole (RFQ) and a chopper line, an Alvarez Drift Tube Linac (DTL), a Cell-Coupled Drift Tube Linac (CCDTL) and a Pi-mode structure (PIMS) [ref 1] (see Fig. 1). This note concerns the vacuum system from the H- ion source to the RFQ.

Page 2: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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Figure 1.Linac4 structure from the source up to the extraction to the PSB (Proton Synchrotron

Booster).

A conceptual scheme of the ion source and LEBT assembly is shown in Figure 3: the

hydrogen injection is regulated by a piezo valve which pulses the gas flow into a first chamber where the ignition of the plasma takes place via a discharge of 600-800 V. Then, the plasma is transferred into the plasma chamber where it is heated using 2 MHz RF up to 100 kW power. A permanent magnet multicusp allows the confinement of the plasma itself, reducing losses on the inner surfaces of the chamber. H- ions are extracted from the plasma by biasing the plasma chamber at -45 kV and grounding the electrode located in the extraction volume. An Einzel lens focuses the extracted ions at the entrance of the Low Energy Beam Transfer (LEBT) line. In the LEBT the H- beam is matched by two solenoids in order to enter the Radio Frequency Quadrupole (RFQ), where it is accelerated from 45 keV to 3 MeV. In addition, as the H- beam tends to expand because of charge repulsion, H2 injection in the LEBT tank is foreseen in order to minimize this effect by space charge compensation.

Figure 2.Linac4 H- source from the source to the RFQ [Ref 2] .

H- Source LEBT RFQ Chopper DTL CCDTL PIMS

45 keV 3 MeV 50 MeV 102 MeV 160 MeV

Source & extraction [600 mm] LEBT [2000 mm] RFQ [3000 mm]

SIP

TMPs

Injection

SOL1 SOL2

LEBT TANK

TMP

Page 3: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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Figure 3.Linac4 H- Source and LEBT [Ref 2]

The H2 gas burst from the piezovalve is about 5*10-3 mbar per pulse; each pulse lasts 5*10-

4s at a repetition frequency of 2 Hz. This gas load has to be pumped in such a way to reach pressures in the 10-8 mbar range in the LEBT without local gas injection for charge compensation. When hydrogen is injected in the LEBT, the pumping system has to ensure working pressures lower than 5*10-7 mbar in the RFQ. In order to cope with these two requirements, three turbomolecular pumps (TMP) of 700 l/s each (nominal pumping speed for N2) are connected to the source: two at the extraction region, and one at the LEBT location. The Einzel lens volume has been designed with a differential pumping geometry to induce a drop in pressure with respect to the extraction region. In addition, it is possible to directly connect to this volume an extra 67 l/s (N2 nominal pumping speed) TMP. In the RFQ, 4 700 l/s TMP, 4 NEG pumps of 2000 l/s (H2) and 4 sputter-ion pumps of 300 l/s (nominal for N2) are connected.

Secondary Vacuum

Extraction Region

Plasma Chamber

Ignition

Piezovalve

Einzel lens

Extra pump connection

TMPS connection

Page 4: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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2. The Electrical Network – Vacuum analogy

To have a good estimate of the 1-D time dependent pressure profile along the source,

the electrical network vacuum analogy has been used [3,4]. This simulation procedure is based on the parallelism between the laws governing voltages in an electrical network and pressures in a vacuum system. There is an immediate correspondence between the equations governing the voltage U and the pressure P drop:

𝑈 = 𝐼𝑅 Eq 1

𝑃 = 𝑄 1𝐶

Eq 2

The voltage corresponds to the pressure; the current I to the gas flow Q; and the resistance R to the inverse of the gas conductance 1/C. For time dependent simulations, it is essential as well to take into account the role of the volume of each component. From the electrical network point of view, this is represented by the introduction of a capacitance to count the amount of charge, i.e. gas, which is stored in the component.

Figure 4 shows the equivalence between simple vacuum components and electrical networks. In the case of a tube, the gas conductance has been divided in two identical parts in order to have a network that is fully symmetrical with respect to the direction of the current flowing into it, i.e. the drop in pressure along a tube is expected to be the same if the flow is injected at one end or at the other.

Figure 4. Electrical Network – Vacuum analogy for simple vacuum components: orifice and tube.

Usually, even a simple vacuum line is composed of several volumes having different shapes and diameters. The electrical analogy is obtained by connecting the equivalent circuits of each element of the vacuum system.

Page 5: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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For example, let us consider a simple system with a tube, an orifice and a pump connected to it as shown in Figure 5. From the standard vacuum calculations point of view, we can estimate the pressure in the vacuum chamber by evaluating the effective pumping speed and the gas load flowing into the system. The effective pumping speed can be estimated by taking into account gas conductance and pumping speed of each element composing the simple system, as follow:

Figure 5.Vacuum system composed of a vacuum chamber, an injection line, a known aperture and a

pumping group

1𝑆𝑒𝑓𝑓

=1

𝑆𝑝𝑢𝑚𝑝+

1𝐶𝑜𝑟𝑖𝑓

+1

𝐶𝑡𝑢𝑏𝑒

Eq 3

The pressure is then given by the usual formula:

𝑃𝑡𝑢𝑏𝑒 =

𝑄𝑆𝑒𝑓𝑓

Eq 4

From the electrical network point of view, a network can be drawn as shown in Figure 6 by connecting the elementary circuits together. The effect of the pump is simulated by the grounding plus a resistor representing the pumping speed of the pump for the gas of interest. The gas load analogy is given by a current source.

Figure 6.Equivalent electrical network, simulating the behaviour of the vacuum system described

above.

Pump

Chamber

Orifice Injection line

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The network can be easily solved with dedicated software (LTSpice, PSpice, etc.). The voltage at the level of the capacitance corresponds to the pressure in the middle of the gas vessel.

Once the equivalent network is assembled, the partial pressures as a function of time can be easily computed in any position of the vacuum system. It is important to underline that these simulations are valid only in molecular flow regime and that each network corresponds to a single gas species, being gas conductance and pumping speed gas dependent.

3. Calculation of the conductance and transmission probability

One of the steps needed in order to evaluate a pressure profile is the calculation of

the conductance of a vacuum component: considering a simple geometry (tube, rectangular duct, elliptical duct...), the conductance can be evaluated as in Eq 5:

𝐶 = 𝜏𝐶𝑎 Eq 5

Where 𝐶𝑎 is the conductance of the aperture of the component, while 𝜏 is the transmission probabillity that a particle entering the component has to exit from the opposite extremity. Tables for the transmission probabilities for simple component (circular, elliptical, rectangular ducts) are available in the literature [5]. For more complex geometry, a dedicated Monte Carlo simulation is used to precisely evaluate the transmission probability. Molflow+ [6], a program written by Roberto Kersevan, is the reference software at CERN for this kind of simulation.

For the LINAC4 source, Molflow was run to evaluate the conductance of complex volumes, as shown in Figure 7 and Figure 8. The first shows one of the inner volumes of the H- extraction region with the boundaries condition set on the entrance and the exit of the component (red circles); the latter is a snapshot of simulated molecular trajectories in the analysed volume .

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Figure 7.Setting boundary conditions for the Monte Carlo simulation on the extraction volumes of

Linac4 H- source.

Figure 8.Particles trajectories interacting with the inner surfaces of the vacuum component.

4. Linac4 H- source: H2 pressure profile

Figure 9a and 9b show the LINAC4 H- source equivalent electrical network. Table 2 summarizes the input parameter for the gas injection pulse used for solving the network. The simulation was run considering H2 as the leading gas.

The red arrows show the correspondence between a part of the source and a part of the electrical network: all the current sources positioned along the electrical path are representing the H2 outgassing from the inner surfaces, even if, considering the significant quantity of H2 injected during each pulse, these sources are negligible. Longer components, e.g. the LEBT and the RFQ tanks, have been divided into three sub-components in order to have a better resolution of the pressure profile.

Pulse Characteristics

H2 Flow 5*10-3 mbar l/pulse

Pulse duration 500 µs

Frequency 2 Hz

Table 1.Input parameters for H2 flow injected in Linac4 H- source.

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Figure 9a: Equivalent electrical network for Linac4 H- source, from the pulsed injection to the end of the RFQ

Page 9: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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Figure 10b: Equivalent electrical network for Linac4 H- source, zoom in the source and extraction region.

Page 10: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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4.1 H2 pressure profiles: results

The following graphs show the H2 partial pressures profiles as a function of time at different positions along the source vacuum line. Figure 11 shows the lowest H2 pressure achievable, considering that the pulsed source is the only gas load in the system. The relevant positions considered are: the middle of the ignition chamber, the middle of the plasma chamber, the extraction volumes (extraction electrodes + Einzel lens), the Low Beam Energy Transfer tank, the entrance to the RFQ, the end of the first, second and third tank of the RFQ. The pressure profile after the first peak is slightly different from those after the following peaks. This is due to the H2 filling of the source volume after the beginning of the first injection.

Figure 11. Hydrogen pressure profiles at 2Hz as a function of the position.

0.0 0.5 1.010-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

P H2

(mba

r)

time (s)

Ignition Chamber Plasma Chamber Extraction region Einzel Lens LEBT Tank RFQ IN RFQ1 RFQ2 RFQ OUT

Linac4 H- Source : best pressures achievable

Page 11: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

- 11 -

Fig. 12 shows that, extending the number of injection cycles, there is no gas accumulation in the system and no pressure build up. Therefore with an injection frequency of 2 Hz, there is enough time left to the system to recover in between two pulses. In other words, the characteristic pumping time of the system is much less than 0.5 s.

Figure 12 : Hydrogen pressure profiles extended over 2.5 s

The pressures calculated in the ignition and plasma chambers are higher than 10-3 mbar. In this pressure range correction should be applied to count for the transition from molecular to viscous regime. However, as already written above, the calculations here reported are carried out only in the molecular regime. As a consequence, the pressure values in the first two vacuum chambers are slightly overestimated. The pressure profile are characterised by the time constants of the different components of the source. The ignition chamber, being the place of injection and having a small volume, fills up before the plasma chamber and the extraction region which are both characterized by bigger volumes, thus, longer filling time. After attaining a maximum value, the pressure in the ignition chamber decreases very fast because the gas accumulated in its volume feeds the nearby plasma chamber. Then, once the plasma chamber volume is filled as well, the time constant of the ignition chamber follows the same profile as the plasma chamber. Finally, as the extraction region is filled, both the ignition chamber and the plasma chamber follow the same time constant as the extraction region where the pumps are installed. The three leading time scales are shown in Fig. 13: in zone I the ignition chamber fills the plasma chamber; in

0 1 210-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

P H2

(mba

r)

time (s)

Ignition Chamber Plasma Chamber Extraction region Einzel Lens LEBT Tank RFQ IN RFQ1 RFQ2 RFQ OUT

H2 partial pressure profiles: build up effect

Page 12: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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zone II, the plasma chamber fills the transition chamber; in zone III the characteristic pumping time of the system leads the transient behaviour.

Figure 13: Hydrogen pressure profiles: zoom in the ignition, plasma and transition chamber profiles.

The study of the ignition and plasma chamber pressure profiles is useful as well for the tuning of the plasma ignition in time. Fig. 14 shows in logarithmic scale of time the pressure transient at the very beginning of the pulse, within which the plasma is foreseen to be triggered.

Fig: 14: Hydrogen pressure profiles: pressure burst during ignition

0.0 0.410-6

10-5

10-4

10-3

10-2

10-1

100P

H2 (m

bar)

time (s)

Ignition Chamber Plasma Chamber Extraction region

1E-5 1E-4 1E-3 0.01

10-4

10-3

10-2

10-1

Pres

sure

(mba

r)

time (s)

Ignition Chamber Plasma Chamber

I II III

Page 13: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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The gas injection in the LEBT strongly affects the pressure profiles from the Einzel lens volume onward (see Fig. 15). The chambers upstream the Einzel lens are not affected by the LEBT injection because their pressure is much higher than the injection pressure. In addition, there are restrictions of aperture located in between the plasma chamber and the Einzel lens where two powerful TMP pumps are installed.

Fig. 15: Hydrogen pressure profiles during injection in the LEBT.

As expected, the LEBT injection affects the pressure in the RFQ tanks. Fig. 16 shows the RFQ H2 pressure profile, along the component, with and without injection in the LEBT. The maximum pressure in the RFQ is about 20 times higher when injecting at 10-5 mbar in the LEBT. The resulting pressure is just higher than the limit of 5x10-7 mbar, but maybe still acceptable. However, if higher injection pressures are needed (for example 10-4 mbar) then the RFQ will experience a maximum H2 pressure higher than the limit.

0.0 0.5 1.010-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

P H2

(mba

r)

time (s)

Ignition Chamber Plasma Chamber Extraction region Einzel Lens LEBT Tank RFQ IN RFQ1 RFQ2 RFQ OUT

H2 injection in the LEBT at 1*10-5 mbar

Page 14: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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Fig. 16: RFQ H2 pressure profiles as function of the position with and without injection at 1*10-5 mbar in the

LEBT.

5. Conclusions

As mentioned, the electrical network – vacuum analogy was applied to the LINAC4 H- source’s vacuum system. The simulated H2 pressure profiles allow a better understanding of the dynamic vacuum behaviour of the source and they set a precise limit in the gas throughput which can be digested by the LEBT (1*10-5 mbar) not to overcome the pressure limit in the RFQ of 5*10-7 mbar. This technique allows as well the evaluation of pressures profile where no pressure gauge can be installed during operation such as the plasma chamber. The calculation have demonstrated that an operation at 2 Hz is compatible with the installed pumping. An experimental campaign of fast pressure measurements is foreseen in the next months in order to fully benchmark the results from these simulations where feasible.

References [1] M. Kronberger, D. Küchler, J. Lettry, Ø. Midttun, M. O’Neil, M. Paoluzzi, and R. Scrivens Rev. Sci. Instrum. 81, 02A708 (2010).

RFQ IN RFQ1 RFQ2 RFQ OUT

1E-9

1E-8

1E-7

P H2

(mba

r)

Position

no injection injection limit

RFQ H2 Profile

Page 15: Vacuum simulation of the LINAC4 H source · Vacuum simulation of the LINAC4 H-source . Chiara Pasquino / TE-VSC, Paolo Chiggiato/ TE-VSC, Jacques Lettry/ BE-ABP . Keywords: electrical

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[2] Courtesy of Didier Steyaert. [3] Susumu Ohta, Nagamitsu Yoshimura, and Haruo Hirano J. Vac. Sci. Technol. A 1 (1) (1983) 84-89; [4] Scott R. Wilson J. Vac. Sci. Technol. A 5 (4) (1987) 2472-2478. [5] J.M. Lafferty, Foundations of vacuum technology (Wiley, New York, 1998), p.89. [6] R. Kersevan and J.-L. Pons J. Vac. Sci. Technol. A 27, 1017 (2009).