#### Beam-Beam Compensation in Tevatron

##### Vladimir Shiltsev

**I. GOAL/POTENTIAL OF THE BBC**

**II. MACHINE PHYSICS**

**A Theory and Tracking of the Beam-Beam Compensation**

**B Tevatron Electron Lens studies with 980 GeV protons**

##  **B.1 The 1^st^ TEL**

##  **B.2 Proton tune shift due to TEL** 

##  **B.3 Proton Lifetime with TEL**

**III. PLANS**

###  

###### [Tev pbars will suffer from linear (bunch-to-bunch) and non-linear tuneshifts]{.underline}

![](media/image1.jpeg){width="8.509722222222223in"
height="3.8402777777777777in"}

Run IIa Run IIb

Linear dQ is proportional to *N~P~*, nonlinear to *N~P~* /ε - both
contribute into peak luminosity as

$$\text{L=}\frac{3\text{}\gamma_{r}f_{0}}{\beta^{}}\left( \text{BN}_{\overline{p}} \right)\left( \frac{N_{p}}{\varepsilon_{p}} \right)\frac{F\left( \beta^{},\theta_{x},\theta_{y},\varepsilon_{p},\varepsilon_{\overline{p}},\sigma_{z} \right)}{(1 + \varepsilon_{\overline{p}}/\varepsilon_{p})}$$

![](media/image2.png){width="6.0in" height="6.016141732283464in"}[What
can be done with Tevatron Electron Lenses (TELs):]{.underline}

a\) - Run IIa 36x36

b\) - with one Linear TEL

c\) - with two Linear TELs

d\) -- two Non-linear TELs

 linear tunespread can be eliminate completely

 non-linear tunespread can be reduced ∼2 times

(Simplistic) estimate of peak luminosity increase

*L∝∆ν*~max~ / (*∆ν*~BB~*+∆ν*~N-Lin~ )

**L-BBC NL-BBC**

Run IIa 16% 60-100%

Run IIb 50% 60-100%

• assuming the same *∆ν*~max~

(no resonances added) and higher N-protons possible

[Non]{.underline}-linear BBC promises additional 2-fold increase in *L
:*

As it may make possible to eliminate the *crossing angle* by
compensating 2 or 4 additional collision points around each IP, thus
increasing geometrical luminosity factor ***L/L~O~*** in Run IIb.

![](media/image3.jpeg){width="7.225in" height="3.938888888888889in"}

• [note:]{.underline} potential increase in the [integrated]{.underline}
luminosity is more modest -- 8-12% due to Linear BBC and some 40% due to
Non-linear BBC

[BBC: Theory and Tracking]{.underline}

The BBC was subject of thorough theoretical analysis and extensive
numerical studies (at peak we employed 1/3 of FNAL computer power) since
1998 and the work is still in progress. Major achievements by now:

• effectiveness of linear BBC is confirmed

• electron beam size and charge distribution are optimized

• misalignment and noise effects are studied

![](media/image4.jpeg){width="4.375in" height="3.240972222222222in"}•
non-linear BBC analysis just started, preliminary results show
possibility of 50% footprint compression without significant resonance
excitation

Figure: P-bar distribution in normalized betatron amplitude plane (A~X~
,A~Y~) after 1 min=3e6 turns \[noise enhanced dynamics\] without (left)
and with TEL (right).

[The 1st Tevatron Electron Lens at F48 (since 03/2001)]{.underline}

• from magnetic measurements we believe that electron beam is straight
within ±0.10mm over 2.5 m of interaction length

• electron current distribution is ∼flat, beam size variable by ratio
B~gun~/ B~main~

![](media/image6.jpeg){width="5.5in" height="4.25in"}

• max current 3.5A, beam energy ∼10 kV, pulse width 800 (100) ns,
f~0~=n⋅48kHz

####### Tuneshift due to Electron Lens

$$\text{dQ}_{x,y} = \mp \frac{\beta_{x,y}}{2\pi} \cdot \frac{1 \pm \beta_{e}}{\beta_{e}} \cdot \frac{J_{e} \cdot L_{e} \cdot r_{p}}{e \cdot c \cdot a_{e}^{2} \cdot \gamma_{p}}$$

**Signs reflect charge of particles and direction of the electron
velocity.**

**L=2.5m long, J=3A, U=7.6 kV electron beam (β~e~** **=0.13 -- somewhat
reduced by space-charge) with radius 1.5mm placed at β~x~ =101m produces
positive tuneshift for 980 GeV antiprotons of about
[dQ=0.01]{.underline}**

[Note]{.underline}: So far we operated the 1^st^ TEL on the protons only
and electrons were moving in the same direction as protons 

For protons (co-moving) 1- β~e~=0.87 ; for pbars (collide) 1+β ~e~ =1.13

### 

### Therefore, we expect smaller and positive proton tuneshift 0.87/1.13=0.77 times the antiproton dQ. 

### 

[Horizontal Schottky spectra of 980 GeV protons]{.underline}

![](media/image8.png){width="6.767361111111111in"
height="6.886111111111111in"}

without electron current

with 3A electron beam

• ***dQ~X~=+*0.0065**

equivalent to *dQ~X~=-*0.0085 for pbars

vertical tune is 4 times less

######## 980 GeV proton hor. tuneshift: theory and experiment 

![](media/image9.wmf){width="9.122916666666667in" height="6.90625in"}

![](media/image10.wmf) **p-tune shifts by TEL: 150GeV, 980 GeV**

[Status of studies:]{.underline} first results instill optimism

> we know a lot about tuneshift --
>
> vs J, U, time, position, angle, e-size

we know something about lifetime

> vs position, angle, WP, J, e-size
>
> we know nothing about emittance
>
> we did not work with antiprotons

[Next step]{.underline}: demonstrate pbar dQ=-0.01 without significant
deterioration of luminosity lifetime. For that:

Find major factors affecting lifetime

Study emittance dynamics

Operate TEL on antiprotons

Improve e-p centering (BPMs, tickling, etc)

Diagnostics/hardware (b-b Q,ε-meter,6A gun, J,X,t-stabilization,etc)

Continue electron beam studies (e.g., space charge effects)

[Time]{.underline}: 6-12 months at 3-4 shifts/months

[Longer Term Scope of the BBC Project]{.underline}

1.  (see short-term plan of studies)

2.  Build and install the 2^nd^ TEL, make the system for Linear BBC
    operational by Oct'03

3.  Attack non-linear beam compensation (studies/hardware/commissioning)
    in FY'04+

4.  Consider crossing angle elimination with TELs (2005?)