COSY experience of electron cooling

V. B. Reva + BINP+COSY teams

BINP, Novosibirsk, Russia, Forschungszentrum, Juelich, Germany

Abstract

The 2 MeV electron cooling

system for COSY-Julich has

highest energy for the electron

cooler with strong longitudinal cooler with strong longitudinal

magnetic field. During operation

the cooling process was detailed

investigated at different energies of

electron beam. The proton beam

was cooled at different regimes:

RF, barrier bucket RF, cluster

target and stochastic cooling. This

report deals with the experience of

electron cooling at high energy.

COSY Accelerator Facility

P=183.6 m, E=2880 MeV

COSY Accelerator Facility- 4 internal and 3 external experimental areas

- electron cooling at low momenta (LM)

-electron cooling at high momenta (HM)

-stochastic cooling at high momenta

βx=6.5 m, βy=3.5 m (High Voltage cooler)

0

10

20

30

βx, βy, D [m]

βx βyHM

LM

gun

collector3D design of high energy COSY cooler

Electrostatic

Accelerator

Transport channel

Design parameters of cooler COSY

2 MeV Electron Cooler Parameter

Energy Range 25 keV ... 2 MeV

Maximum Electron Current 1-3 A

Cathode Diameter 30 mm

Cooling section length 2.69 m

Toroid Radius 1.00 m

Magnetic field in the cooling section 0.5 ... 2 kG

Vacuum at Cooler 10-9 ... 10-10 mbarVacuum at Cooler 10-9 ... 10-10 mbar

Available Overall Length 6.39 m

Electron cooling was investigated at following energies

Proton energy, MeV Electron energy, keV Max. electron current, A

200 109 0.5

353 192 0.5

580 316 0.3

1670 908 0.9

2300 1250 0.5

no cooling

IPM monitor

Schottky signal from pick-upSignal from Ion Profile Monitor

coolingbefore

cooling

First cooling experiment - cooling at

Ee=109 keV Longitudinal cooling

Transverse cooling

cooling

normal cooling

instability

Large intensity and low momentum spread may induce coherent instability

Jp≈0.18mA Jp≈0.25mA

0 100 200 300 400 5000

2

4

6

8

“First problem with coherent instability” t, s

1

2

3 4

1 – vertical width (mm)

2 – horizontal width (mm)

3 – proton beam current (0.1 mA)

4 – electron current (100 mA)

Increasing of proton intensity switch on

the instability. It can be observed in the

transverse plane and pickup spectrum

both

Ee=109 keV

0.5

1

1.5

2

2.5

1

2

3

4

5

6

7

8

Next step - cooling at Ee=192 keV, electron current 300 mA

cooling time is ∼ 150 s

Cooling switch off

A, mm

1

2

3

4

×10-4 σ=δps/p (rms)

Exponential

approximation

cooling time is ∼ 20 s

Cooling switch off

100 200 300 400 500 6000.50 100 200 300 400 500 600 700

1

Transverse cooling

Longitudinal cooling

Transverse size versus time: 1 and 2 are

horizontal and vertical width of proton

beam, 3 is exponential estimation of

cooling time горизонтальная ширина

пучка, 4 – is expansion of proton beam

with diffusion coefficient 3⋅10-2 мм2/c.

t, s t, s

Longitudinal momentum spread (r.m.s)

versus time.

“First call” – transverse cooling

may be worse than longitudinal one

-0.4 -0.2 0 0.2 0.40

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Next step - cooling at 315.85 keV, electron current 300 mA

-0.80 -0.53 -0.27 0.00 0.27 0.53 0.80

71

142

213

285

356

427

498

569

×10-3 σ=δps/p ×10-3 σ=δps/p

t, s

t=10 s

t=15 s

t=30 s

switch off

e-beam

Spectrogram of the longitudinal distribution function longitudinal distribution function

very fast

long. cooling

0 100 200 300 400 500 6000.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5 10 15 20 250

5

10

15

20

25

30

35H/V, mm

hor

ver

hor, arb. unit

mm

t=5 s

t=190 s

switch off

e-beam

t, shorizontal and vertical width versus time

Spectrogram of the longitudinal distribution function

versus time. Levels are intensity of Schottky signal

horizontal profile before and after cooling

longitudinal distribution function

Larmour rotation can be essential for the cooling process

0.4 0.60.20.0-0.4

-0.2

0.0

0.2

∆X, mm

∆Y, mm

edip kick=+1/0 A edip kick=+2/0 A

-300 V 0 +300 V -300 V 0 +300 V

0.2LR mm= 21 1.59eE

mcγ = + =

2

1.7e

cool

m ccm

eB

γβρ = =

0

0.012e Lp R

p

δρ

⊥ = =

1275coolB G=

The electron energy is changed according schedule.

315.85 (0 s) → 316.15 (100 s) → 315.55 (300 s) → 315.85 (500 s).

The cycle duration is 600 sec.

Observation cyclotron rotation of the electron beam with BPM at changing

of magnetic field (i.e phase shift of motion) in the cooling section.

max 0.7 2.7i flightv mmρ τ= = −

316eE keV=

Jump of electron energy for estimation cooling rate

Maximum experience - cooling at 909 keV,

electron current up to 900 mA,

many good experimental results was obtained

Fast longitudinal cooling

1

1.5

2×10-4 σ =δps/p (rms)

Exponential approximation

0.015

0.02

0.025

F(σ)

60 s

120 s

100 200 300 400 5000

0.5

1

t, s-0.4 -0.2 0 0.2 0.4

0

0.005

0.01

×10-3 σ= δps/p

0 s60 s

Base experiment parameters

Np=4⋅108, Ep=1.67 GeV, γtr=2.26

Ee=909.05 keV, Je=520 mA, Uan=5.3 kV, Ugr=0.4 kV, Magnetic field in the cooling section Bcool=1380 G

τcool=40 s

Longitudinal momentum spread (r.m.s)

versus time

longitudinal distribution function for the different

moments of cooling process

0 100 200 300 400

1

1.5

2

2.5

3

3.5

hor

H/V, mm

ver

τ=100 s

Best transverse cooling at high energy

Schottky signal from pick-up

0 100 200 300 400

t, s

3.6·108 protons, 1.66 GeV Ie = 0.8 A 1.3 kG

1. Noise + EC, 2. Noise only, 3. Reference, 4. EC

1 23

4

time

hor/ver, mm

Ee=909 keV

100 kHz f0=1.52 GHz

Cooling of bunched proton beam on COSY. Electron energy 908 keV. Electron current 0.5 A.

Measurements

Simulations with

Parkhomchuk’s

equation and space

charge field

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Electron cooling can well operate with usual RF

Cooling simulations for COSY

-400 -200 0 200 4000

t, ns

1.5238 1.5239 1.5240

0.01

0.02

0.03

0.04

0.05

0.06

F, GHz

Fitting curves of the shape of the proton bunch for the start (left picture) and

the end (right picture) of the cooling process. RF on, e-cooling with 570 mA, Np=2∙109,

Ee=909 kV

0

20

40

60

V, mV

12

t=0 s

100

200

V, mV

123

t=500 s

0

85s nsσ =

16s nsσ =

1 is experimental profile, 2 is gauss shape, 3 is parabolic shape

The estimation of the length according equation gives the length 14 ns that is very

close to the experimental data. So, the beam core attains equilibrium induced by the

space charge force.

e-cool can help to obtain the space-charge limit

( )3 2

3 2 2

2ln 1

2

p

s

RF

beN

a

Uσ

π γ

+ = Π

0.5 0.6 0.7 0.8 0.9t, sµ

0.6 0.7 0.8t, sµ

0

e-cool can well operate with usual RF and target Ee=909 kV, Np=2⋅109, na =2∙1014 cm-2

Next step - cooling at 1259 kV

Changing energy of electron beam to 100 V that corresponds to dp/p=6⋅10-5. The equilibrium

momentum of proton beam is changed also that can be easily observed with Schottky spectrum

analyzer.

0.0351.6

×10-4 σ =δps/p (rms) F(σ)

Example of the longitudinal cooling at 1259 kV

-0.4 -0.2 0 0.2 0.40

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 100 200 300 400 5000.2

0.4

0.6

0.8

1

1.2

1.4

t, s ×10-3 σ= δps/p

0 s

180 s

90 sτcool∼90 s

Momentum spread versus time Evolution of the longitudinal distribution

function during cooling process

Barrier Bucket + e-cool Barrier Bucket + e-cool+targetElectron cooling with barrier bucket and target with density Ee=1259.5 kV, na =2∙1014 cm-2

e-cool can well operate with barrier bucket and target

Barrier Bucket + e-cool Barrier Bucket + e-cool+target

Experiments with target without electron cooling

Target has a significant influence on the dynamic of the proton na =2∙1014 cm-2

target

Spectrogram of Schottky noise at target action. The top picture shows ionization loss in cluster

target corresponding to hydrogen density na =2∙1014 cm-2. The bottom picture shows the

simultaneously action barrier bucket and target. All spectrum duration is about 550 s.

target + barrier bucket

Electron energy 1259.65 kV, Je=500 mA Experiments with e-target

E-cool + target

target

Electron cooling suppressed the longitudinal action of the target with density na =2∙1014 cm-2

without help RF.

∆p/p =4.3 10-4

T=620 s

Electron cooling

practically suppressed

longitudinal and

transverse growth

induced by target but

the more precise

tuning storage ring

0 200 400 600 800 1000 1200 14001.5

2

2.5

3

0 200 400 600 800 1000 1200 14001.5

2

2.5

3

target

target

E-cool +

target

E-cool +

target

V, mm

tuning storage ring

and e-cooler is

necessary.

H, mm

1. Dominance of the longitudinal friction force. The longitudinal cooling

is more easy for realization

2. Essential influence of the Larmour oscillation of electron beam to

Next part of this report is more about puzzle and

features that was observed during operation.

transverse cooling rate at high energy but the longitudinal cooling rate

was observed practically the same

3. Changing equilibrium momentum of proton beam at excitation of

Larmour oscillation of electron beam

4. Influence of the angle between electron and proton beam on the

transverse cooling rather than longitudinal cooling

5. Role of the collective phenomena at electron cooling of the proton

beam to the small momentum spread of the proton beam

17:34 17:38

18:47 19:07

Milestones of the first cooling at new energy of the electron beam (1.25 MeV )

Weak shift to new energy Ee=1256 keV More strong shift to new energy Ee=1256.6 keV

∼570 s∼570 s

18:47 19:07

First cooling at new energy Ee=1259.5 keV Good cooling at new energy Ee=1259.55 keV

∼400 s∼400 s

After ∼ 1.5 hours the longitudinal cooling process was obtained at new energy 1259.5 keV (after

series experiments at 909 keV energy). The situation with transverse cooling isn’t such optimistic.

proton number

is 2∙109

horizontal

position, mm

vertical

position, mm

Transverse e-cooling at 1259 kV energy

Changing transverse size during

43

38

43 Maximum attention was given to

looking for a working point of

storage ring where the electron

cooling had maximum effectiveness.

The transverse cooling process was

observed after spending much time

and efforts.

position, mm

horizontal

width, mm

vertical

width, mm

600 s

1

600 s 600 s

Changing transverse size during

cooling experiments. Curve 1 is

reference cycle without cooling ,

curve 2 is cooling at energy 1259

kV, curve 3 is growth of the

transverse size at changing working

point despite of electron cooling

action. Tune was shift at ∆Qx/ ∆Qy

≈ 0.02/-0.01 (estimation).

2 3

1

3

2

338

1

2

x 10×10-4 σrms

edipver1=2.71A

-1.4

-1.3

-1.2

-1.1

-1

-0.9×10-3 mm/s, δcool

horizontal cooling decrement

Essential influence of the Larmour oscillation to transverse cooling

rate but the longitudinal cooling rate was observed the same

momentum spread versus time

100 200 300 400 500 6000

t, s

2.11 A

Main parameters of experiment

Electron energy is Ee=907.7 keV

Proton energy is Ep=1.67 GeV

Anode and grid voltages are Uan=3.27, Ugr=0.83 kV,

Electron current is Je=600 mA,

Magnetic field in the electron gun is 230 G, acceleration column is 400 G, collector is 500 G. Longitudinal

magnetic field in the cooling section is 1300 G, in the toroid section is 1200 G, bend magnet is 860 G.

Slip-factor of the proton beam is η= -0.035.

The number of proton is Np=1.6-1.8⋅109.

2 2.2 2.4 2.6 2.8-1.6

-1.5

edipver1, A

Amplitude of the Larmour oscillation was changed with help

of corrector coils with short longitudinal length – edipver 1.

1 A of corrector current may excite Larmour

oscillation with radius 0.35 mm

0.5

1

1.5

2

2.5

3

-1

-0.5

0

0.5

1x 10

δcool=1/τcool

heating

cooling

×10-3 mm/s, δcool

Another example of influence of Larmour oscillation to transverse cooling rate. It is

possible to eliminate transverse cooling but the longitudinal decreases not so much

×10-4 σ =δps/p (rms)

-2.32

-2.72

-2.92 (transverse = heating)

δcool>0

δcool<0

100 200 300 400 5000

0.5

Parameters of the experiments Ee=907.7 kV, Je=595 mA, Uan=3.27, Ugr=0.83 kV

-3 -2.8 -2.6 -2.4 -2.2 -2 -1.8-1.5

-1

horizontal cooling decrement

If the Larmour rotation is strong enough it can kill the transverse cooling. The longitudinal

cooling time is increased but it present.

t, sediphor1, Alongitudinal momentum spread versus time

for different value of current in electron

dipole corrector ediphor1

-1.92

-7 -6 -5 -4 -3 -20

0.005

0.01

0.015

0.02

0.025F(σ)

-1.92

-2.12

-2.32-2.52

-2.72

-2.92

It is interesting that the correlation between changing of the dipole corrector and equilibrium

momentum of the proton beam. Figure shows the distribution function of the protons in time

500 s for the different value of ediphor1 corrector. Increase the transverse momentum

(Larmour oscillation) leads to

decrease the longitudinal momentum3909 10eE keV= ⋅ 1380coolB G= 0.35LR mm=

21 2.78eE

mcγ = + =

2

3.2e

cool

m ccm

eB

γβρ = =

2

5

0

16 10

2

II Lp R

p

δδσ

ρ−

= = = ⋅

The quality behavior is good. The quantitative

difference can be explained that the transverse

motion already has nonzero amplitude of Larmour

0

0.011e Lp R

p

δρ

⊥ = =

-7 -6 -5 -4 -3 -2

×10-4 σ =δps/p

0 500 1000 1500 2000 2500-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 500 1000 1500 2000 2500-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

s, cm s, cm

Demonstration of excitation of Larmour oscillation of electron induced by edip corrector.

ediphor=optimum+0 A ediphor=optimum+1A

x/y, cmx/y, cm

RL=0.35 mm

motion already has nonzero amplitude of Larmour

oscillation.

Cooling

section x,y orbit of the electron

from accelerating to

decelerating tube along

electron cooler

(simulation)

1

1.5

2

2.5

×10-4 σ= δps/p, (rms)

-1.7

-1.6

-1.5

-1.4

-1.3

×10-3 mm/s, δcool horizontal cooling decrement

τcool∼60 s

Essential influence of the incline of the magnetic force line to

transverse cooling rate with compare to longitudinal rate

0 100 200 300 400 5000.5

t, s0.1 0.2 0.3 0.4

-1.8

coolver, A

horizontal cooling decrement longitudinal momentum spread versus time

Changing angle between electron and proton beam with coolver corrector. This corrector

induces the transverse magnetic field along whole cooling section. It leads to incline the

magnetic force line and electron beam in the cooling section.

50.1 4 10coolverJ A δθ −= → ≈ ⋅ 0.1coolL mmδθ ⋅ ≈ 2700coolL mm= 1380coolB G=

Parameters of the experiments Ee=907.7 kV, Je=595 mA, Uan=3.27, Ugr=0.83 kV

So, fine tuning needs for transverse cooling but not for longitudinal cooling .

0.002

0.004

0.006

0.008

0.01

0.012

0.014

460

F(σ)

t=960 s 600

670

759

Longitudinal electron cooling. The electron current is changed at fixed ratio Ugrid/Uan

Np=4.7⋅108, Je=600 mA, Ugr=0.83 kV,

Uan=3.27 kV, Ee=907.9 kV

The longitudinal cooling rate isn’t strongly depend

from the electron current value.

Example of the fitting of the core of the proton beam.

The fixed ratio Ugrid/Uan allows to suppose that the

regime of the electron gun isn’t changed.

Role of the value of electron current

Drift of equilibrium energy is induced by space charge

of electron beam.

-5 -4 -3 -2 -1 0 10

×10-4 σ= δps/p

-5 -4 -3 -2 -1 0 10

0.002

0.004

0.006

0.008

0.01

0.012

0.014

×10-4 σ= δps/p

F(σ)

Gauss fit

σfit=1.8⋅10-5

experimental data,

t=960 s, Je=600 mA

200 400 600 800 10000.5

1

1.5

2

2.5

x 10×10-4 σrms

t, s

RMS momentum spread

versus time. The growth

of the momentum spread

is induced by the tail un

the distribution function.

Example of the fitting of the core of the proton beam.

The main part of particle has a small momentum spread.

1.5

2

2.5

3

1

1.5

2

2.5

hor, mm ver, mm

460 mA

600 mA (green)

670 mA (red)

760 mA (blue)

460 mA

600 mA (green)

670 mA (red)

760 mA (blue)

Transverse electron cooling. The electron current is changed at fixed ratio Ugrid/Uan

Role of the value of electron current

200 400 600 8001

200 400 600 8000.5

t, s t, s

460 mA – Ugrid=0.7 kV Uanode= 2.72 kV Ugrid/Uanode=0.257

600 mA – Ugrid=0.83 kV Uanode= 3.27 kV Ugrid/Uanode=0.254

670 mA – Ugrid=0.9 kV Uanode= 3.54 kV Ugrid/Uanode=0.254

759 mA – Ugrid=0.98 kV Uanode= 3.86 kV Ugrid/Uanode=0.254

One can see that the transverse cooling suffer from electron current decreasing especially for Je=460 mA

The transverse cooling more depend from the electron current value.

1.9

2

2.1

2.2

-5 -4 -3 -2 -1 0 10

0.002

0.004

0.006

0.008

0.01

0.012

Collective effects (fact or myth) ?

ecool off

Np=2.3⋅109

Np=2.3⋅109300 s

400 s

580 s

×10-4 σ =δps/p

intJ=∫J(f)df, arb. units

ecool Np=2.0⋅109

Np≈2.1⋅109

The most experiments shows long tails in the longitudinal

distribution function. This tails slowly move during all

time of experiment. What is the reason ?

0 200 400 600 8001.6

1.7

1.8

no ecool

Je=600 mA, Ugr=0.83 kV, Uan=3.27 kV, Ee=907.9 kV0 200 400 600 8000

0.5

1

1.5

2

2.5

x 10

t, s

×10-10 ∫J(f)df

×1Np=5⋅108

Np=2.3⋅109

ecool on

t, sA possible criterion of collective effect is integral of

Schottky signal along whole spectrum range. At presence

of the collective effect this integral is larger in comparison

with the situation when all particle is independent (no

collective fluctuation) and the integral of power of

Schottky signal is proportional to the particle number.

2

3

4

5

6x 10∫J(f)df, arb. unit

Np=2.7⋅108

Np=1.2⋅109

1

2

x 10

Np=1.2⋅109

Np=2.7⋅108

×10-4 σrms

The changing of integral of Schottky signal at electron cooling is more

clear at precooling with transverse stochastic cooling

Switch off stochastic cooling

Switch on electron cooling

σ =δps/p

200 400 600 8000

1

t, s

∫J(f)df – integral of power of Schottky signal along whole

frequency range. If the particle motion is independent the

integral is constant. The collective mode of particle oscillation

changes this result.

200 400 600 8000

Time schedule

000 s – switch on the transverse stochastic cooling

200 s– switch on the electron cooling with current 600

mA, switch off the transverse stochastic cooling

∼ 700 s – switch off the electron cooling (no cooling at all)

800 s – switch on the electron cooling again

t, s

Preliminary stochastic cooling increase particle density so the collective effect may be more visualized

We may observe the normal situation. Decreasing momentum spread leads to decreasing Landau

damping. Let pay more attention to impedance problems

Momentum spread pf the proton beam versus time

transverse stochastic cooling

electron cooling

Stochastic precooling strongly improve the ultimate parameters

of proton beam

0 100 200 300 400 5001

1.5

2

2.5

0 100 200 300 400 500

0.8

1

1.2

1.4

1.6

1.8

2H, mm V, mm

experiment 2

experiment 1

experiment 2

experiment 1

Np=1.1⋅109.

0.60 100 200 300 400 500

1

0 100 200 300 400 5000

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500

t, s t, s×10-4 σrms

t, s

transverse stochastic cooling

experiment 1

experiment 2

experiment 2

experiment 1

longitudinal stochastic cooling

electron cooling

After stochastic precooling procedure the size of the

proton beam may be cooled down to minimal value.

Also the longitudinal momentum spread may be

decreased to very low value. The electron cooling can

be operated with transverse stochastic cooling together

simultaneously.

0.6

σ =δps/p

0.002

0.004

0.006

0.008

0.01

0.012

1

1.5

2

2.5

3

H/V mm, σ ×10-4

×10-4 σ (rms)

ver

hor

180 s

F(σ)

4 s

300 s

Np=3.3⋅108,

Ee=907.9 kV,

Je=600 mA

800 s

Longitudinal stochastic and electron coolingThe joint action electron and longitudinal stochastic cooling doesn’t change the distribution function (180 and

300 s profiles). The r.m.s. spread after 550 s depends from tail and doesn’t show the cooling of bulk protons.

longitudinal

stochastic cooling

σ =δps/p

-4 -2 0 2 4 60

0 200 400 600 8000.5

t, s

000 – turn on longitudinal stochastic cooling

200 – turn on electron cooling with current 600 mA

300 – turn off longitudinal stochastic cooling

380 – turn on longitudinal stochastic cooling

550 – turn off longitudinal stochastic cooling

×10-4 σ

-4 -3 -2 -1 0 1 20

0.002

0.004

0.006

0.008

0.01

0.012

0.014

experimental

profile 800 s

Gauss fit

σ (fit, gauss) = 1.4⋅10-5

×10-4 σ

F(σ)

The electron cooling isn’t very effective in joint with longitudinal

stochastic cooling. But the cooling power of electron cooling is

strongly. The mail part of proton can be cooled to momentum

spread σ = 1.4⋅10-5

.

stochastic cooling

electron cooling

Screenshot of oscilloscope. The barrier bucket RF signal is magenta, signal from Schottky pick (longitudinal beam shape)

up is blue. The time after start of the experiment is about 420-450 s.

Np=1⋅109, Je=600 mA, Ee=908.085 kV, na=2.0 ⋅ 1015 см-2

Stochastic, electron cooling, barrier bucket RF and dense target

Electron and transverse stochastic cooling Longitudinal and transverse stochastic cooling

So, the electron cooling helps to keep the longitudinal shape of the proton beam at action of

dense target

2

3

4

5

6

7

Unfortunately the single action of the electron cooling at high density target is not enough

with point of view of transverse cooling

0

1

2

3

4

5

6

x 10H/V mm, ×10-4 σrms

×10-4 σ (rms)

ver

hor

20 s

90 s

300 s

590 s

×10-3 F(σ)

×10-4 σ (rms)

without cooling

100 200 300 400 500 6002

Np=1.7⋅109, Je=600 mA, na=2.0 ⋅ 1015 см-2Time schedule

000 s – start of barrier bucket RF, p-p 1100 V

030 s – turn on electron cooling with current 600 mA,

100 s – turn on target

-2 -1 0 1 20

t, s

One can see that the electron cooling isn’t enough for strong transverse cooling. It leads to decreasing

of the longitudinal cooling rate. The start of growth of momentum spread is postponed to 100 s

because the it need time for energy lost of particle in order to escape from RF well

×10-3 σHorizontal, vertical sizes and momentum spread of the

proton versus timeHorizontal, vertical sizes and momentum spread of the

proton versus time

BUT the longitudinal cooling is strong despite of the growth of transverse size

from 2.7/2.3 to 6.8/4 mm.

Only electron cooling

Summary

1. COSY experience of use of electron cooling shows that it is

enough powerful method in the different region energies

2. The electron cooling may work well together with, target, RF,

barrier bucket RF and stochastic cooling

3. The physics of electron cooling may contain an open question

and the puzzle with 50 years history may have unopened area.

4. Understanding of physics behavior of the transverse cooling may 4. Understanding of physics behavior of the transverse cooling may

improve transverse electron cooling to compare today situation.

5. The simple optimization of transverse cooling optimization can

be connected with increase of the beta function in the iteration

point.