1. Managed by UT-Battelle for the Department of Energy CERN 4 th TLEP Mini-Workshop 2013 Longitudinal Beam-Beam Effects at TLEP (Novosibirsk Phi factory experience recollection); Resistive wall instabilities (VLHC experience ->TLEP, LHeC). V. Danilov SNS AP group

2. 2Managed by UT-Battelle for the Department of Energy Presentation_name Talk outline  History of the finding  Underling physics  Basic formulas, big picture, estimations for LEP3 and TLEP  Transverse resistive wall instabilities: a) Closed Orbit Instability; b) TMCI; c) Other effects.

3. 3Managed by UT-Battelle for the Department of Energy Presentation_name Longitudinal beam-beam kick history 1) In 60 beam-beam colliders saw first beam-beam effects; 2) The origin was thought to be the transverse effects; 3) Then longitudinal modulation of the transverse kick was thought to be most important; 4) Derbenev, Skrinsky (around 1970) started to think if energy change is possible in beam-beam collisions; 5) 1972 – they publish the first paper on longitudinal beam-beam effects; 6) The effect was small for the first collider and then long forgotten; 7) The effect was recalled in 80s in Novosibirsk when high-luminosity colliders were considered; 8) My recollection – approximately the same time Koji Hirata (KEK) started the same development; 9) I was asked to advance the topic and get general formulas for the kick not only on axis (as in Derbenev, Skrinsky) – 1991 paper; 10) Below I follow its derivation of the kick extending calculations to flat beams;

4. 4Managed by UT-Battelle for the Department of Energy Presentation_name Simplified physics e-e- e+e+ IP E On axis Head of bunch energy decreased – acts like defocusing cavity for positive momentum compaction e+e+ IP E e-e- Trailing particle energy Increased – valid only for electron-positron collisions General case 1 2 1 2 Same particles Red-gets energy Blue-gives energy to red The exchange happens Not at the same time

5. 5Managed by UT-Battelle for the Department of Energy Basic Formulas (1) Presentation_name Integrate with Gaussian transverse distributions Round beam, first term agrees with Derbenev, Skrinsky (1972)

6. 6Managed by UT-Battelle for the Department of Energy Basic Formulas (2) Presentation_name Important for simulations - not only to account for energy change, But to preserve symplecticity Recent addition – flat beam  x  y On-axis result: Same as round beam with reduced number of particles. Ratio of sizes is an extra factor that indicates which particles contribute to the energy change

7. 7Managed by UT-Battelle for the Department of Energy Coherent Effects Presentation_name Consider short bunches (length shorter or comparable to the IP beta function k is the coefficient of voltage reduction The threshold for unstable coherent behavior twice as lower as in Incoherent motion – with the particle increase we’ll see first the coherent instability

8. 8Managed by UT-Battelle for the Department of Energy LEP3/TLEP estimations Presentation_name For LEP3 For TLEP (given by F. Zimmermann) The results are about 3 orders of magnitude less Than the gradients of the planned RF

9. 9Managed by UT-Battelle for the Department of Energy Synchro-betatron motion with e-kick Therefore, the effect for TLEP from synchrotron motion is in modulation of betatron phase with the longitudinal position and energy, but the kick has to be always included into simulation to preserve symplecticity.  Very peculiar growth of particle amplitudes was found and later described in “Negative momentum compaction in the longitudinal beam-beam effects” V.V. Danilov V.V. Danilov, E.A. Perevedentsev, D.N. Shatilov (Novosibirsk, IYF), HEACC 1992E.A. PerevedentsevD.N. ShatilovNovosibirsk, IYF ds=  dE, d  b =  -ds/    0 (dE is the energy change due to one collision; particle has large angle) Presentation_name

10. 10Managed by UT-Battelle for the Department of Energy Resulting Loss of Particles (D. Shatilov) Presentation_name Novosibirsk old phi-factory projectNegative momentum compaction

11. 11Managed by UT-Battelle for the Department of Energy Resistive wall instabilities  1 Type – Closed Orbit Instability – extreme number of particles (more relevant to LHeC);  Classical TMCI (more relevant to TLEP);  Very Large Hadron Collider experience – resistive wall wake is dominant because of general trend of size and cost reduction (its contribution grows like inverse cube of vacuum chamber radius);  All instabilities are most important and calculated at injection energy of 10 GeV. Presentation_name

12. 12Managed by UT-Battelle for the Department of Energy Extreme case-closed orbit instability  Fields so high they distort the orbit;  Discovered while we worked on SNS Ring (Danilov, et al, PRSTAB 2001);  The threshold ;  LHeC: Nth=7*10 13 ({nu}=0.5); Design 6*10 13 ;  TLEP: Nth=5.5*10 12 ({nu}=0.04); Design 9*10 12 – the working point has to be further away from integer Presentation_name

13. 13Managed by UT-Battelle for the Department of Energy TMCI – Transverse Mode Coupling Instability Presentation_name VLHC mode diagram This instability was present in LEP at injection energy

14. 14Managed by UT-Battelle for the Department of Energy Basic TMCI – 1 bunch instability  Short bunch – resistive wall wake contribution is large 1/sqrt(length) – probably, dominant wake;  Beam Stability Issues in Very Large Hadron Collider A. Burov, J. Marriner, V. Shiltsev ∗, FNAL, Batavia, IL 60510 V. Danilov, ORNL, Oak Ridge, TN 37831 G. Lambertson, LBL, Berkeley, CA 94720 NIM 2000  b- is the vacuum chamber radius – critical parameter (determines cost and stability) Presentation_name

15. 15Managed by UT-Battelle for the Department of Energy TLEP threshold  Nth TLEP=1.8·10 10 at injection – 40 times below the design value;  Mitigation – injection synchrotron tune should be increased 10 times;  The length at injection has to be larger;  Some other possibilities? Presentation_name

16. 16Managed by UT-Battelle for the Department of Energy Other associated transverse problems  Since Closed Orbit Instability threshold is close, no doubt there are multi bunch instabilities;  Requires feedback;  VLHC problem – detuning wake cause large spread of betatron tunes. It could be fatal for the beam (important for LHeC and TLEP);  Shape of the vacuum chamber determines it and its important to optimize it. Presentation_name

17. 17Managed by UT-Battelle for the Department of Energy Vacuum chamber – round or elliptical?  To cope TMCI – synchrotrone tune ≈1  Betatron tuneshift ≈1, the betatron incoherent tune spread due to detuning wake is around 1. Integer and half-integer resonance crossing- low beam lifetime.  Round VC – no detuning wake. But bad from dispersion/energy acceptance; space consideration.  Maybe there exist solution with round cavity and accordingly shaped poles? Presentation_name

18. 18Managed by UT-Battelle for the Department of Energy Presentation_name Conclusion  Low IP beta high current factories encounter new type of effects – large energy change due to fields of counter beams, but because of very high RF gradients, the energy change effect is negligible for TLEP as compared to low energy Phi-factory;  Resistive wall wake become large for short bunches – the TLEP thresholds at injection are low; the injection should be taken care of;  Closed Orbit instability threshold is close to the design number of particles -an integer resonance should be avoided;  Detuning wake can cause a large spread of particle’s tunes – needs to be worked on.