sponge-metal beam optimized iners - arturo stabilecause thermal runaway and quenching of...

Commissione V – Riunione del 24 - 28 Settembre 2012, Roma

SPONGE-metal Beam Optimized Liners

Stefania Petracca Arturo Stabile Vincenzo Pierro

Sezione di Napoli Gruppo collegato di Salerno


Outline

Synchrotron Radiation Issues : LHC and beyond

Open Cell Metal Foams Technology, Modeling Tools

OCMF for Beam Liners: Potential Benefits Vacuum, Impedance, SEY

The SPONGE-BOL Research Plan Goals, Working Group, Collaborations, Budget, etc


Synchrotron Radiation Issues : LHC and Beyond

Synchrotron radiation induced molecular gas desorption from the beam-pipe wall should be properly taken into account in the design of high energy particle accelerators and storage rings. Nuclear scattering in the residual gas would limit the beam luminositity lifetime, and eventually cause thermal runaway and quenching of superconducting magnets.

Synchrotron radiation is also responsible of e-cloud formation phenomenon, which may also severely limit the achievable luminosity/energy goals [K.C. Harkay, “Observation and Modeling of Electron Cloud Instability ,” Proc. EPAC '06, paper WEXFI02 (2006)].

This has been a major (solved) challenge for the Large Hadron Collider ["The Large Hadron Collider Conceptual Design," CERN Rept. AC/95-05 (1995)].

It will be even more critical for the HE-LHC, in view of its higher level of synchrotron radiation [A. Valishev, "Synchrotron Radiation Damping, Intrabeam Scattering and Beam-Beam Simulations for HE-LHC,“ arXiv:1108.1644v1 [physics.acc-ph] (2011)].

It will be crucial for the successful operation of the proposed electron-positron Higgs factories [A. Blondel et al., "LEP3: A High Luminosity e+e- Collider to Study the Higgs Boson,“ ArXiv: 1208 .0504v2 [physics.acc-ph] (2012)]

36 mm tall

44 mm wide


The LHC Beam Screen

●In the LHC a copper-coated stainless-steel beam pipe kept at 20K by active He-cooling, handles the heat load represented by synchrotron radiation, photoelectrons, and image-charge losses. ● A large number (102 m-1) of tiny slots drilled in the liner wall keep the desorbed gas densities below a critical level (1015 molecules m-3 for H2), allowing desorbed gas to be continuously cryopumped toward a co-axial stainless-steel tube (magnets’ cold-bore) kept at 1.9K by superfluid He.

● Size, geometry and density of the slots affect the beam dynamics and stability through the long- itudinal and transverse beam coupling impedances. The slots pattern the hole pattern should be designed to prevent coherent buildup of leaking synchrotron radiation in the waveguide limited by the beam pipe and the cold bore


Outline






Open-Cell Metal Foams


OCMF Technology

Open - cell metal foams are produced either by (vapor or electro) deposition of metal on an open-cell polymer template, followed by polymer burn/off, and final sintering step to densify the liga- ments. Alternatively, they are obtained by in infiltration/casting of molten metal into a solid mould, consisting of packed (non-per-meable) templates of the pores, followed by burn-out and rem- oval of the mould. Both processes result into highly gas-permeable foam, where only a 3D web of solid conducting struts among the pores survives.

The key morphological parameters of OC metal foams foams are the pore size ( 10-3 – 10-4 mm typ), and the porosity (vol fraction of pores, 08-0.99 typ)

[J. Banhart and N.A. Fleck, "Cellular Metals and Metal Foaming Technology,“ MIT Press (2003)]


OCMF Materials and Manufacturers

• Al and Cu OC-foams are now available off-the-shelf; • Foam coating (e.g., with Ag, Ti or Pt) is possible; • OC-foams using Ag, Ni, Co, Rh, Ti and Be, as well as alloys (e.g., Steel or Brass) are feasible; • Several Manufacturers worldwide (e.g., ERG/Aerospace, Goodfellow (USA); Mitsubishi (JP); Lyrun (CHN); Universal Metaltech (IN), Dunlop (UK), M-Pore (DE), and more…


OCMF Structural Modeling

• The Weaire-Phelan (WP) space-filling honeycombs are credited as the natural (i.e., Plateau's minimal surface principle compliant) model of a reticulated metal with equal - sized (and possibly un-equal-shaped) pores.

The WP unit cell consists of a certain arrangement of (irregular) polyhedra, namely two pentagonal-face dodecahedra (with tetra-hedral symmetry Th) , and six tetrakaidecahedra, featuring two hexagonal and twelve pentagonal faces (with antiprysmatic sym-metry D2d) …


Wearie-Phelan cell (left), and its building blocks (right),

numerically generated Wearie-Phelan foam

[D. Weaire and R. Phelan, Phil. Mag. Lett. 69 (1994) 107]

OCMF Structural Modeling, contd.


OCMF Typical Structural Properties

[Courtesy ERG Aerospace]


OCMF Bulk Electrical Conductance

In the limit where bubbles and metal struts are much smaller than the (smallest) wavelength of interest, the conductivity of a metal foam can be computed using effective medium theory (EMT) [F.G. Cuevas et al., J. Por. Mater. 16 (2008) 675]. Several EMT formulations exist, e.g.

• infinite dilution approximation (non-interacting inclusions subject to the field • self-consistent approach (inclusions embedded in the sought effective medium);

• differential approach (inclusions added incrementally – infinite dilution approx

at each step); • effective field approach (interaction among the inclusions described in terms of a matrix or matrix+inclusions - averaged field).

[Y. Qui and G.J. Weng, Int. J. Eng. Sci.28 (1990) 1121; S.K. Kanaun, Int. J. Eng. Sci. 41(2003) 1287 ]

[D.A.G. Bruggemann, Ann. Phys. 24(1935) 636]

[R. Goodall et al., J. Appl. Phys., 100 (2006) 044912]


OCMF Bulk Electrical Conductance, contd.

…all models merge in the p 0 limit. Differential approach result (2) agrees with a percolative model …

1)

2)

3)

Infinite dilution & self-consistent appr.

Differential approach

Effective field approach (MT&LK)

matrix (bulk) metal conductivity

Porosity (bubble volume fraction)

Morphology dep- endent factor

[I. Sevostianov et al., Mater. Sci. Eng. A420 (2006) 87]


OCMF Cryogenik Bulk Conductance


Outline






Vacuum Dynamics

[O. Grobner, Vacuum 60 (2001) 25]

To be kept below some critical values…

liner volume per unit length

liner surface per unit length

number of molecules desorbed from wall by synchrotron radiation per unit length and time

number of molecules removed By wall/sticking or hole/escaping per unit length and time

number of molecules sticking to wall, per unit length and time

number of wall-sticking molecules recycled by thermal activation or radiation per unit length and time

volume density of desorbed particles

surface density of desorbed particles

(compare to eqn. for a)

h

h At equilibrium ( )

desorption yield

specfic photon flux

average mol. speed

wall sticking probability

hole escape probability

radiation-induced recycling coeff

molecular vibrational frequency

activation energy

h


Vacuum

[O. Grobner, Vacuum 60 (2001) 25]

Typical values (Solid portion of wall, LHC, Hydrogen)

s


Vacuum / Perforated vs OCMF Wall

[S. Petracca et al., PR-STAB 2012 in print]

Perforated, solid metal wall Open-cell metal foam wall

Hole/escape probability:

Thin wall:

Thick wall:

𝑓ℎ =surf. covered by holes

total wall surf.= 𝑓ℎ

(0)

𝑓ℎ = 𝜒𝑓ℎ(0),

Clausing factor [R.P. Iczkowski et al. J. Phys. Chem. 67(1963) 229]

𝑤 = wall thickness, 𝑅ℎ = hole radius

A typical value for 𝒇𝒉 𝐜𝐚𝐧 𝐛𝐞 ≈ 𝟎. 𝟎𝟒

Porosity 𝜌ℎ (volume fraction of voids) as a function of avg. voids radius 𝑅ℎ and voids volume density 𝑁ℎ

Surface density of voids Avg. surface of wall holes

Can be ≈ 𝟎. 𝟕 for typ. porosities (𝝆𝒉 ≈ 𝟎. 𝟖)

Fraction of wall surface covered by holes (0)

Trabecular structure of material → Lambert- Beers reduction factor (must agree w. Clausing in the 𝑤 → 0 limit)

𝑓ℎ = 𝑓ℎ(0)𝑒𝑥𝑝 −𝑤/2𝑅ℎ

…


Vacuum / Perforated vs OCMF Wall, contd.

[S. Petracca et al., PR-STAB 2012 in print]


Also, sticking probability will be 𝑟𝑒𝑑𝑢𝑐𝑒𝑑, 𝑠 → 𝑠 1 − 𝑓ℎ since molecules can only stick to the solid fraction of the wall surface;

Also, expect smaller recycling factor 𝜅, as synchrotron radiation will not penetrate the OCMF wall beyond a few skin-depths 𝛿𝑠, so that only a fraction of molecules sticking to the metal inside the foam could be recycled.

Potentially, overall better


Beam Coupling Impedance / Perforated vs OCMF Wall


Simplest case: circular pipe of radius b , on-axis beam (order of magnitude estimation)

≈ ≈ ; (parasitic loss)

[S. Petracca, Part. Acc. 50 (1995) 211]

[S.S. Kurrenoy, Particle Accel. 39 (1992) 1; [S. Petracca, Phys. Rev. E60 (1999) 6030]

Thin wall:

vacuum impedance

electric (e) /magnetic (m) hole polarizabilities density of holes

Thick wall: 𝛼𝑒,𝑚 → 𝛼𝑒,𝑚 𝑒𝑥𝑝 −𝜉𝑒,𝑚𝑤

cut-off attenuation constant (TE/TM) of hole waveguide

𝜎𝑒𝑓𝑓

effective OCMF bulk conductivity

The synchrotron radiation power leakage through the OCMF liner can be estimated as

can be used to estimate beam coupling impedances , and parasitic loss .

𝛿𝑠 = 2/𝜔𝑠𝜇𝑜𝜎𝑒𝑓𝑓1/2

being the effective skin depth.

Potentially not worse, or even better

Randomness of pores helps reducing risk of coherent build up of leaking radiation


SEY / Perforated (rough) vs OCMF Wall

(Perforated) ”rough” solid metal wall Open-cell metal foam wall

Secondary emission yield known to be effectively reduced by making the wall rough, e.g. by "scrubbing“ the surface by high - energy particle bombardment, or powder blasting . Higher depth-to-spacing and dwell width-to-thickness ratios in the scrubs yield smaller SEY.

(No thin/thick wall comparison available) Potentially comparable

[I. Montero et al., Proc. CERN AEC '09, paper #29 (2009), M. Pivi et al., SLAC Pub. 13020 (2007)]

morphologies morphology

typical SEY vs energy

• Small accessible solid wall fraction • SEY reduction energy dependence ?


Outline






SPONGE-BOL Goals

• Wideband modeling of relevant electrical properties (surface impedance, skin depth) of OCMF, including comparison between numerical (Finite Element Integration Technique) and analytic (Effective Medium Theory) approaches.

• Wideband electrical characterization (Microwave Vector Network Analyzer) of OCMF prototypes. Dependance of results on OCMF structural parameters (pore-size and porosity, bulk conductance).

Available results refer to low-frequency (EMI applications) in Literature

• Characterizing vacuum-relevant parameters of OCMF (collaboration w. CERN).

Only high/flux (Avionics) results available in Literature

• Characterizing dependence of OCMF SEY on structural parameters (collaboration

w. CERN and LNF)

No result available yet in Literature

• Developing modeling/simulation and design-optimization tools for beam-liners using OCMF insets, w. specific reference to beam/coupling impedances, vacuum and SEY properties.

• Testing of a prototype HE/LHC specs compliant beam liner using OCMF insets (collaboration w. CERN).


Support from CERN (BE)


SPONGE-BOL Working Group/Collaborations

Collaborazioni:

CERN BE Department / LHC

dr. Frank Zimmermann,

dr. Giovanni Rumolo

INFN-LNF

dr. Roberto Cimino

LAL

dr. Theo Demma


SPONGE-BOL Time Table and Budget

Numerical (FEM) and analytic (EMT) modeling of the electrical properties of open cell metal foams, vs pore size and porosity.

30/6/2013

Wide-band measurement of surface impedance on OCFM samples. Measurements of vacuum related parameters (collab. CERN); measurements of SEY vs energy (collab. LNF) for different pore sizes and porosities.

31/12/2013

Simulation codes for computing beam coupling impedances, synchrotron radiation leakage, vacuum steady state properties and e-cloud dynamics collab. CERN, LAL) in a beam-pipe using OCFM insets.

30/6/2014

Experimental characterization (beam coupling impedances, vacuum properties, SEY) of a prototype HE/LHC compliant beam-liner using OCMF insets.

31/12/2014

Travel to CERN Prototyping Costs

1st year 5K EUR 10K EUR

II anno 5K EUR 10K EUR

sponge-metal beam optimized iners - arturo stabilecause thermal runaway and quenching of...

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