Thermal-Mechanical Analysis of the RF Structures for the ELI-NP Proposal

V. Pettinacci (INFN Roma) - D. Alesini, L. Pellegrino (INFN-LNF) - L. Palumbo (“Sapienza” University of Rome)

Abstract The room temperature RF structures, in the ELI-NP linear accelerator, will operate in multi-bunch with high repetition rate (100 Hz). For these reasons they are subject to some kW of power dissipated on the internal cavities surfaces. The resulting thermal deformation of the cavities shapes could imply variations in their electromagnetic fields. To limit these effects and optimize the cooling design, a fully coupled Electromagnetic-Thermal-Mechanical analysis has been performed on the S-Band Radiofrequency Gun and on the C-Band multi-cell structures. In this paper the study done in Ansys Workbench with HFSS and Ansys Mechanical is reviewed.

S-band Gun It’s used in the first stage of electron beam generation and acceleration (photo-injection). They are standing wave (SW) copper cavities feed by RF klystrons and operate in the range of 100-130 MV/m peak accelerating field on the cathode.

Electro-Magnetic Design The RF gun studied is a 1.6 cells gun, operating on the TM010-like accelerating mode, with field phase advance per cell π. The electrons are emitted on the cathode through a laser (hitting the surface) and are then accelerated trough the electric field, presenting a longitudinal component on axis. The gun, presently under study (Fig.1), is able to operate at 100 Hz with 1 kW of dissipated power.

Main improvements: •  Iris profile has an elliptical shape and a larger aperture; •  N.2 deformation tuners on the outer wall of the full cell; •  Coupling window between the rectangular waveguide and the full cell rounded; •  Cooling pipes have been improved and increased in number, to guarantee a better gun temperature uniformity; •  Structure has been realized without brazing but using special gaskets in order to maintain hard copper (instead of soft copper resulting from

brazing process at high temperature) to reach higher accelerating field with lower BDR.

Thermal-Mechanical Design

C-band Module In ELI-NP Gamma Beam System, the LINAC energy booster is composed of 12 travelling wave C-Band structures, 1.8 m long with a field phase advance per cell of 2π/3 and a repetition rate of 100 Hz.

The goal of the mechanical design is to define a cooling pipes system, able to get a uniform temperature distribution and a consequent homothetic deformation of Gun body, in order to maintain the nominal EM field configuration. Two complementary approaches (Fig.2) have been followed: •  Steady-State Thermal Analysis with Line Bodies to calculate the heating of

the coolant and of the body (“Straightforward model”); •  Totally coupled Steady-State Thermal and Static Structural Analysis, using

the previous results as part of the boundary conditions for the temperature and deformation field calculation, and closing the loop in HFSS, to evaluate its effect on the internal EM field (“Loop model”).

Straightforward model: HFSS and Steady-State Thermal analysis. In the first analysis the EM model geometry has been refined, designing the cooling channels inside the body and the toroidal slot for the cathode cooling; the EM field has been imported as Heat Flux (W/m2) on the internal cavity surfaces. The convective exchange coefficient derives from the Gnielinski correlation, valid for a wide range of Reynolds number [6]. Water velocity inside tubes is set to 1 m/s; this value derived from considerations about channels pressure and corrosion problems. Higher values of fluid velocity, until 3 m/s, could be in case adopted. An APDL section has been added in the Steady-State Thermal module of ANSYS Workbench, to implement the heat exchange across the channels walls, plus the natural convection with air on the external surface.

The temperature distribution calculated in the Gun (Fig.3) presents: •  ΔTGun ≈ 3.8 °C •  T max Gun = 32.8 °C.

The maximum temperature variation of the coolant (fresh water, Fig.4) calculated is: •  ΔT water max ≈ 1.9°C  

Loop model: totally coupled analysis HFSS, Steady-State Thermal and Static-Structural. The goal of the model is to calculate the total deformation, due to thermal load acting on the body, and its effect on the EM field configuration, including their mutual influence. In this kind of analysis, up to now, is not possible to use the modified Line Bodies. For this reason the previous model results have been used to set the temperature for small segments of each cooling tube, for a fixed coolant temperature convective calculation.

Maximum Total Deformation ≅ 0,036 mm (Fig.5). Closing the loop analysis on the HFSS module, this deformation entails a -400 kHz shift of the Reflection Coefficient resonant peak (Fig.6). The Gun works as a resonant and accelerating structure only if this peak is close to nominal generators frequency (2.856 GHz), in order to absorb the RF impulses (without reflecting them) and accelerate electrons.

Electro-Magnetic Design On this module nominal power dissipated is 2.3 kW. The dimensions of each cell have been carefully optimized to simultaneously obtain: •  the lowest peak surface electric field on the irises; •  an average accelerating field of 33 MV/m with an available power from the klystron of 40 MW (Fig.8); •  the largest iris aperture compatible with the previous points to increase the pumping speed of the structure, to reduce the dipole wake-field

intensity and the filling time of the structure itself.

Structure type Quasi-Constant gradient

Working frequency (fRF) 5.712 [GHz] Number of cells 102 Structure length 1.8 m Working mode TM01-like Iris half aperture radius 6.8 mm-5.78 mm Cell phase advance 2π/3 RF input power 40 MW Average accelerating field 33 MV/m Acc. field struct. in/out 37-27 MV/m Average quality factor 8850 Shunt impedance 67-73 MΩ/m Phase velocity c group velocity (vg/c) 0.025-0.014 Filling time 310 ns Output power 0.3*Pin Pulse duration for beam acceleration (τBEAM)

<512 ns

Rep. Rate (frep) 100 Hz Pulsed heating <6oC Average dissipated power 2.3 kW Working temperature 30 deg

Thermal-Mechanical Design Departing from results of HFSS analysis (Heat Flux imported, W/m2), basically the same approach of Gun analysis, has been followed, with the same 2 complementary simulations carried out: •  Steady-State Thermal Analysis with Line Bodies, to calculate the heating of coolant (water fresh) and main body, constituted by 102 copper cells

brazed (“Straightforward model”); •  Totally coupled Steady-State Thermal and Static Structural Analysis, using the previous results (coolant temperature distribution along tubes) as

part of the boundary conditions for the temperature and deformation field calculation, evaluating its effect on the internal EM field once closed the loop in HFSS (“Loop model”).

The main design features of the thermal model are: •  8 cooling tubes, ID=10 mm; •  Coolant velocity 1 m/s and running counter-flow (4 opposite to the other 4); •  Given the symmetry respect the XZ and YZ plane (Z beam axis), only ¼ of structure has been modelled, reducing computing requirements.

Straightforward model: HFSS and Steady-State Thermal analysis. The EM field has been imported as Heat Flux (W/m2) on the internal cavity surfaces. Line Bodies have been designed coaxial with the cooling tubes, modifying their elements through dedicated APDL section, inserted at the end of the Steady-State Thermal analysis tree in ANSYS Workbench.  Natural  convec-on,  with  room  temperature  air,  has  been  imposed  on  the  external  surface  and  the convective exchange coefficient for tubes derives, also in this case, from the Gnielinski correlation [6].

The temperature distribution calculated in the cells assembly (Fig.9) presents: •  ΔT Cells ≅ 3 °C •  T max Cells ≅ 26 °C

The maximum temperature variation of the coolant (fresh water, Fig.10) calculated is: •  ΔT water max ≅ 0.9°C  

Loop model: totally coupled analysis HFSS, Steady-State Thermal and Static-Structural. In this analysis the goal was calculation of C-band structure deformation (thermal load acting on the internal surfaces) and its effect on the EM field configuration, including their mutual influence. As well as done for the Gun, Line Bodies have been suppressed and the previous model results have been used to set the temperature for small segments of each cooling tube. Frictionless supports have been set at the symmetry planes and at one end of the structure, to simulate the free elongation along the Z-axis.

The deformation calculated (Fig.11) presents the main component in the axial direction (Z-axis): the maximum is about 0,053 mm. Indeed, the maximum deformation calculated on the inner surfaces, in radial direction, is about 1.2 μm . After the loop closing in HFSS, no relevant shift has been observed in the frequency domain.

Figure 1 – RF Gun HFSS design Table 1 – RF Gun properties

Table 2 – C-band structure RF properties

Figure 2 – ANSYS Workbench Analyses Schematics

Figure 3 – Gun copper body temperature distribution Figure 4 – Cooling water temperature distribution along tubes

Figure 5 – Gun body total deformation (heat load) Figure 6 – Reflection coefficient resonant peak frequency shift Figure 11 – C-band structure (heat load effect): deformation (longitudinal Z, transversal X, transversal Y)

Figure 9 – C-band structure: copper cells temperature distribution Figure 10 – C-band structure: coolant temperature distribution

Figure 7 – Drawing of travelling wave C-band structure

Figure 8 – Accelerating electric field on axis

References [1] D. Palmer PhD thesis “The next Generation Photoinjector”, June 1998. [2] D. Palmer, R. H. Miller, et al, SLAC-PUB-95-6800. [3] ELI-NP TDR, under publication, 2014. [4] D. Alesini, et al., THPRI042, this conference. [5] “Thermal Analysis of a Radiofrequency Gun”, D. Alesini, L. Pellegrino, V. Pettinacci, L. Ficcadenti – UGM 2013 Ansys Inc. ("Innovabook 2014" - Paper Anthology, Fluidodinamica, Meccanica, Elettromagnetismo - Cobalto Casa Editrice). [6] F.P. Incropera, D.P. Dewitt, “Fundamentals of heat and mass transfer” 5th ed., J. Wiley and son, 2002.

Parameters Value Resonant frequency fres 2.856 GHz Unloaded quality factor Q

0 15000

Repetition rate 100 Hz Coupling coefficient β 3 Shunt impedance (R) 1.78 MΩ Filling time τF 420 ns Frequency separation between the 0 and the π-mode

38 MHz

Average dissipated power 1 kW

Conclusions The room temperature RF structures in the ELI-NP LINAC will are subject to some kW of power dissipated on the internal cavities surfaces due to the 100 Hz operation. The cooling systems have been designed to get homothetic deformations on the RF structures. For the S-Band Gun there will be the necessity to cool down the inlet water temperature by about 8°C (using a local chiller), in order to keep the structure on resonance. For the C-band structures the calculations results entails negligible deformations in the radial dimensions of the cells (about 1.2 μm in the worst case) while the deformation main component is along the longitudinal Z-axis and the overall maximum deformation integrated on the 102 cells is about 0,05 mm. As a consequence, a negligible frequency shift has been calculated.

Acknowledgements We would like to thank A. Battisti and V. Lollo (INFN-LNF), for their technical support in CAD design stage of the RF structures described.