andrea.mostacci@uniroma1.it beam-wall interaction in the lhc liner: a former phd student experience...

Andrea.Mostacci@uniroma1.it

Beam-Wall Interaction in the LHC Liner:

a former PhD student experience

A. MostacciLa Sapienza, University of Rome

Francesco Ruggiero Memorial Symposium, 3 October 2007

Andrea.Mostacci@uniroma1.it

Francesco believed in the need of the SL-AP group of preserving and transmitting AP know-how. When he became group leader, training of students was explicitly declared in the SL-AP group mandate.

I had the honor to be one of Francesco’s students.

Francesco as my PhD thesis supervisorFrancesco as my PhD thesis supervisor

… I learnt from him a method.

He was always looking for the physical insight of results, first condition for them to be correct.

The first step to assess a result was to always look for a counter-example.

The need (and the pleasure) to understand in depth the issues that we were dealing with.

Constant in-depth discussions during all my thesis work.

Ability of highlighting the critical points in my work and recommending clever following steps.

Warm atmosphere for young people in the group.

Andrea.Mostacci@uniroma1.it

LHC beam pipeLHC beam pipe

Andrea.Mostacci@uniroma1.it

LHC beam pipeLHC beam pipe

Pumping holes.

Artificial (saw-tooth) roughness.

Weldings.

Interaction between the beam and a surface (synchronous) wave in a (rectangular) beam pipe with “small” periodic corrugations.

Currents distribution in a (metallic) beam pipe whose conductivity varies with the azimuth (ultrarelativistic beam).

EM coupling, through holes, between a cylindrical and a coaxial waveguide.

Andrea.Mostacci@uniroma1.it

LS

kQcP

b

2

bS bunch spacing

L device length

• Ohmic losses in the coaxial region:

• Holes and equivalent dipoles (Modified Bethe

Theory).

• Polarizability including also the wall thickness.

• Coupling impedance (beam stability).

• Loss Factor k() (energy losses).

• Power lost per unit length: P.

b internal radius d external radius

r.m.s bunch length

2 d

2 b

resistivity

Pumping holes in a coaxial beam pipePumping holes in a coaxial beam pipe

.

Andrea.Mostacci@uniroma1.it

• Randomising the position of the holes does not affect the loss factor.

• Ohmic losses in the coaxial region:

• Limit of negligible ohmic losses (N equispaced holes, at distance D) :

magnetic polarizability

electricpolarizability

Pumping holes: loss factorPumping holes: loss factor

.

.

Andrea.Mostacci@uniroma1.it

100 300 500 700

0.2

0.6

1

Plin

P

PmW/m

Length (m)

Plin no attenuation

LHC parameters

P limit value

P “exact” formula

A. Mostacci, L. Palumbo and F. Ruggiero, Physical Rev. ST-AB (December ‘99).

Pumping holes: power lost per unit lengthPumping holes: power lost per unit length

Andrea.Mostacci@uniroma1.it

2

1.5

10.6 0.8 1

1

5

1015

W (mm)

T (mm)

Curves of constant power per unit length (mW/m)

A. Mostacci and F. Ruggiero, LHC Project Note 195 (August ‘99).

Around LHC nominal values ():

WTExpPP 75.1 0

4

0 5.1 / 42

mm

WmmWP

W slot width (rectangular)

T wall thickness

.

,

Pumping holes: impact on the liner designPumping holes: impact on the liner design

Power loss per unit length is negligible for holes of the nominal dimensions.

Andrea.Mostacci@uniroma1.it

0 p€€€€€2

p 3 p€€€€€€€€€€2

2 p

123456

Beam pipe with azimuthally varying conductivityBeam pipe with azimuthally varying conductivity

• Cylindrical geometry (circular cross section).

• Leontovich conditions (SIBCs):S/m107

n=1

)(

b

,

.

.

.

/2 /2following an approach proposed in

F. Ruggiero, Phys. Rev. E, Vol. 53, 3, 1996

Andrea.Mostacci@uniroma1.it

0 p€€€€€2

p 3 p€€€€€€€€€€2

2 p

0.20.40.60.8

1

0 p€€€€€2

p 3 p€€€€€€€€€€2

2 p

0.20.40.60.8

1

Stainless steel / “cold” copper

1 GHz

1 MHz

20 kHzn=1 n=1

• Ultrarelativistic limit.

• From B.C, we get a system for the coefficients (truncation).

• Semi-analytic solution.

• A posteriori check of B.C.

mm FF~

,

Stainless steel / “warm” copper

Azimuthally varying conductivity: solution (I)Azimuthally varying conductivity: solution (I)

/2 /2/2 /2

Andrea.Mostacci@uniroma1.it

100

105

1010

1015

0

0.2

0.4

0.6

0.8

1

FrequencyBoundary conditions validity limits (no anomalous skin effect).

Room TemperatureCryogenic Temperature

Azimuthally varying conductivity: solution (II)Azimuthally varying conductivity: solution (II)

Surface currents are constant over the azimuth (at all the relevant frequencies). The losses in the welding is 5 % of the ones in the copper at room temperature (50% at cryogenic temperatures).

Andrea.Mostacci@uniroma1.it

0 0.5 1 1.5 2-0.6

-0.4

-0.2

0

0.2

0.4

0.6

H zH

A/m

z/

• Wire method.

• f = 1 GHz, P = 1 W.

• No solution inside the conductor.

Azimuthally varying conductivity: simulation (HFSS)Azimuthally varying conductivity: simulation (HFSS)

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Azimuth. varying conductivity: Q measurements (I)Azimuth. varying conductivity: Q measurements (I)

Coaxial resonator:

Q measurements in

various configurations.

F. Caspers, A. Mostacci, L. Palumbo and F. Ruggiero, LHC Project Note 493 (August ‘01).

Andrea.Mostacci@uniroma1.it

Francesco’s legacyFrancesco’s legacy

Respect and promote young people’s work.

Intellectual honesty and rigour.

Many small and practical tips which I still pass on to our students.

Ability to give meaningful comments or suggestions on many technical aspects of several accelerator physics problems.

Andrea.Mostacci@uniroma1.it

Francesco’s legacyFrancesco’s legacy

I am proud to have been one of Francesco’s students. I am proud to have been one of Francesco’s students.

Respect and promote young people’s work.

Intellectual honesty, rigour and attention to details.

Many small and practical tips which I still pass on to our students.

Ability to give meaningful comments or suggestions on many technical aspects of several accelerator physics problems.