theoretical and experimental challenges

QED in laser-plasma interactionstheoretical and experimental challenges

Tom BlackburnChalmers University of Technology

4th July 2017Workshop on Plasma Astrophysics From the Laboratory to the Thermal Universe

Introduction

Goals

Understanding QED in laser-plasmas is necessary

Understanding QED in laser-plasmas is interesting

(Understanding QED in laser-plasmas is difficult)

Introduction

Goals




Introduction

Goals




Introduction

Quantum electrodynamics

Fundamental theory of the interaction between light and matter

Unifies quantum mechanics with special relativity

Charged particles interact via the emission and absorption of photons

Introduction





Introduction


Each vertex carries a factor of e the electron charge and a δ-function encoding the conservation of momentum

Simplest two photon emission (radiation reaction) and pair creation

Introduction


Two-photon pair creation (Breit-Wheeler process) not observed experimentally (heavy ion collisions hohlraums)

Multiphoton Breit-Wheeler seen at SLAC (50 GeV electron beam into 1018 Wcm-2 laser 140 positrons) Non-linear index n = 5 6

Introduction

What are the challenges

QED in strong electromagnetic fields

Coupling QED to classical plasma physics

Experimental observation with currently available laser systems

Introduction





Reduce a hard problemby splitting it into a ldquoeasyrdquo part and a ldquosmallrdquo correction

Results take the form of a series expansion around the easy (ie unperturbed) solution

eg ground state energies in quantum mechanics

Beyond perturbative QED

Perturbation theory in quantum mechanics






Stark effect Coulomb potential perturbed by static electric field

Zeeman effect Coulomb potential perturbed by static magnetic field




Energy shift of the ground state of H







More = better



More = better





More = better



More = better





But the series diverges






Perturbation theory generically leads to divergent series

This has been known for a long time ndash see Bender and Wu Phys Rev 184 1231 (1969)

Besides infinities are interesting



ldquoThe series is divergent therefore we may be able to do something with itrdquo - O Heaviside

ldquoThis is infinity here It could be infinity We donrsquot really donrsquot know But it could be It has to be something ndash but it could be infinity rightrdquo- D J Trump



We can handle divergent series using Borel summation










Use the integral definition of a factorial





Swap the summation and integration



What does this mean for factorially-divergent series




If the terms alternate in sign the result is real and finite





If they dont the integrand has a pole on the real axis






This has physicalsignificance



Recall the dispersion relation for an EM wave in a warm plasma

The permittivity has a pole where the phase velocity of the wave and the particle velocity are equal

Gives rise to Landau damping




If the terms do not alternate in sign Borel summation gives you an imaginary term that is non-perturbative in the coupling strength

Non-perturbative in the sense that exp(-1x) has Taylor expansion about 0 that is 0 to all orders




Divergent perturbative series with coefficients that do not alternate in sign


Divergent perturbative series with coefficients alternating in sign











Ionization rate





Perturbation theory is generically divergent

Controlling those divergences naturally introduces physics from the non-perturbative sector

Why non-perturbative





Why non-perturbative Why perturbative



Does the same occur in quantum field theory

After all perturbation theory has proved extraordinarily successful




Perturbation theory in QED

Static magnetic field Euler-Heisenberg effective action (exact result)




Perturbative expansion is divergent but the signs alternate



Static electric field The field invariants are E2 ndash B2 and EB






Transform B2 rarr ndashE2 and the terms no longer alternate in sign







S has a non-perturbative imaginary part





The action for a static electric field acquires an imaginary part that is non-perturbative in the electric field strength

Stark effect = ionisation rate Here we get the pair-creation rate from the vacuum

Ecrit = 13times1018 Vm



How do we access fields of this magnitude in the lab

Important parameter is χ (ratio of electric field in electron rest frame to the critical field of QED)


QED in intense fields

χ = 1 means the electron sees in its rest frame a field strong enough for non-perturbative effects to dominate

Low order terms are suppressed only high order terms (ie involving large numbers of background photons) contribute



Treat the intense background as a classical field calculate transition rates to all orders




Rates no longer diverge but now we need entire space-time structure of the background field





What about arbitrary field structures



Introduction





If the formation length is short enough we can assume the fields are quasi-static over the emission process

The formation length is smaller than the laser wavelength by a factor of the strength parameter a0

Coupling sfQED and classical processes

Locally constant field approximation





What do we lose by doing this

Harmonics sub-harmonics interference resonanceshellip

When is it acceptable to do so

How much bigger than 1 must a0 be



Other constraints on PIC simulations

Size of timestep must be set to avoid multiple scatterings (constraint set by rate of photon emission is strongest)

C P Ridgers et al J Comp Phys 260 273 (2014)

The rates (not cross-sections) for photon and pair production are calculated in an equivalent system of fields with the same instantaneous value of χ

eg a static magnetic field in the ultrarelativistic limit T Erber Rev Mod Phys 38 626 (1966)


PIC + Monte Carlo

We assumed a classical background field

Contains sufficient energy that the field is not affected by a (single) QED process

Energy is absorbed by plasmas ndash what happens to the background field



Creation of electron-positron pair transfers energy from background field (at interaction point)

χ 1 photon energy split evenly between electron and positron

For χ 1 most goes to one of the electron and positron


Depletion

Example photon collides with a single-wavelength linearly-polarized plane EM wave

Beyond the background field approximation

Depletion


For χ 1 quantum depletion 2m2ω vs classical a0

2m2ω


Depletion



2m2ω

For χ 1 quantum depletion m vs classical a0

2m


Depletion


Laser absorption is increased (classically) because QED processes introduce new currents


Depletion

In QED need to calculate transition rates between initial and final states that contain different numbers of photons

Does the LCFA let us take a simpler approach to calculating the effect of a QED avalanche on the background field


Depletion

When does the quantum depletion have a serious effect on the background

Seipt et al PRL 118 154803 2017 for electron-beam laser collision need 10nC and a0 of 1000

Effects on angular distribution at lower intensity


Depletion

Introduction





Positron production

Test bed

Electron-positron pair creation by the collision of high-energy particles with an intense laser pulse

eg wakefield accelerated electrons bremsstrahlung created gamma rayshellip

In the highly non-linear regime

Positron production

Test bed

Interaction can be modelled directly from QED (Di Piazza PRL 117 213201 2016)

Integrated full-scale QED-PIC simulations for wakefield acceleration plus photon and pair creation (Lobet et al PRAB 20 043401 2017)

Positron production

Scaling laws

Can obtain analytical expressions for the photon spectrum the energy of those that pair create and the positron energy

Total number of positrons is given by the integral of the photon spectrum weighted by the pair creation probability

Positron production

Scaling laws



Positron production

Scaling laws

Necessary collision parameters

To create 100 positrons from 100 pC of charge need

for a 30fs pulse

Positron production

Scaling laws

Synchronisation and overlap between the beams

Beam size effects theory predicts 10500 pairs from collision between 100pC electron beam (2 GeV 10 micron size) and laser pulse I21 = 5 800nm wavelength and 2 micron waist 3D PIC gives 10000

Many theoretical questions remain how to account for back-reaction and multiphoton effects self-consistently in QED

How will the answers to those questions inform simulation development Is the QED-PIC model sufficient

Experimental work is of critical importance ndash and can be done with currently available laser systems

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Introduction

Goals




Introduction

Goals




Introduction

Goals




Introduction





Introduction





Introduction




Introduction




Introduction





Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






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Introduction

Goals




Introduction

Goals




Introduction





Introduction





Introduction




Introduction




Introduction





Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






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Introduction

Goals




Introduction





Introduction





Introduction




Introduction




Introduction





Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






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Introduction





Introduction





Introduction




Introduction




Introduction





Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






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Introduction





Introduction




Introduction




Introduction





Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






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Introduction




Introduction




Introduction





Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






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Introduction




Introduction





Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

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Introduction





Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

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Introduction



























More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

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More = better



More = better





More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

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Slide 81

Slide 82



More = better



More = better
















































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

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Slide 31

Slide 32

Slide 33

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Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82














































































Ionization rate







































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

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Slide 28

Slide 29

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Slide 32

Slide 33

Slide 34

Slide 35

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Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82



































































Introduction

























PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

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Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

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Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82





















PIC + Monte Carlo










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82










Depletion



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 16

Slide 17

Slide 18

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Slide 20

Slide 21

Slide 22

Slide 23

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Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

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Slide 36

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Slide 53

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Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82



Depletion



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

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Slide 13

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Slide 19

Slide 20

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Slide 31

Slide 32

Slide 33

Slide 34

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Slide 53

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Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82



2m2ω


Depletion



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

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Slide 36

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Slide 41

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Slide 49

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Slide 51

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Slide 53

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82



2m2ω


2m


Depletion




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

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Slide 41

Slide 42

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Slide 46

Slide 47

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Slide 51

Slide 52

Slide 53

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Slide 57

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82




Depletion




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 23

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82




Depletion





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82





Depletion

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

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Slide 36

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Slide 40

Slide 41

Slide 42

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Slide 51

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Introduction





Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

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Slide 10

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Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Positron production

Test bed




Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

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Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Positron production

Test bed



Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

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Slide 50

Slide 51

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Positron production

Scaling laws



Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Positron production

Scaling laws



Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

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Positron production

Scaling laws



for a 30fs pulse

Positron production

Scaling laws






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Positron production

Scaling laws






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theoretical and experimental challenges

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