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QED IN ULTRA-INTENSE LASER FIELDS ∗ T. Heinzl † , School <strong>of</strong> Computing & Mathematics, University <strong>of</strong> Plymouth, UK C. Harvey, A. Ilderton and M. Marklund, Department <strong>of</strong> Physics, Ume˚a University, Sweden Abstract We present an overview <strong>of</strong> basic QED processes in the presence <strong>of</strong> an ultra-intense laser background. INTRODUCTION The year 2010 has seen the 50th anniversary <strong>of</strong> the laser. Since its inception it has undergone a very dynamic development culminating in a multitude <strong>of</strong> everyday applications. From the physics point <strong>of</strong> view specification parameters have evolved in many directions, for instance towards the X-ray regime <strong>of</strong> frequency. For the purpose <strong>of</strong> this conference and this talk we are particularly interested in ultrahigh intensities. The historical development <strong>of</strong> these is pictured in Fig. 1 (adapted from [1]) with a notable breakthrough in 1985 due to the implementation <strong>of</strong> chirped pulse amplification (CPA) [2]. Figure 1: Time evolution <strong>of</strong> laser intensity. The vertical axis on the right-hand side measures intensity I in terms <strong>of</strong> the dimensionless laser amplitude a0 = eEλ mc 2 ∼ I1/2 , (1) which is the energy gain <strong>of</strong> an electron (charge e, mass m) across a laser wavelength λ in the r.m.s. field E, in units <strong>of</strong> its rest energy, mc 2 . Hence, when a0 exceeds unity an ∗ Work supported in part by ERC, Contract No. 204059-QPQV. † theinzl@plymouth.ac.uk electron probing the laser field will begin to move relativistically. It is worth pointing out that ultra-intense lasers produce the largest electromagnetic fields that are currently available in the lab. Of course, the downside is that the fields are pulsed (i.e. “short-lived”) and alternating. An overview <strong>of</strong> the current magnitudes is given in Table 1. Table 1: Some typical current magnitudes. Quantity Magnitude Power P 10 15 W ≡ 1 PW Intensity I 10 15 W/cm 2 Electric Field E 10 14 V/m Magnetic Field B 10 10 G Planned facilities where these magnitudes will be increased further include the Vulcan 10 PW project at the Central Laser Facility <strong>of</strong> Rutherford Lab, UK and the European Extreme Light Infrastructure where up to 100 PW are envisaged. STRONG FIELDS: THEORY We are interested in elementary processes occurring in the presence <strong>of</strong> an ultra-intense laser. The appropriate theory is (a variant <strong>of</strong>) strong-field quantum electrodynamics (QED) with the laser field being included as an external background field. The extent to which this theory is under analytical control depends sensitively on the model chosen for the laser beam. The simplest model is an infinite, monochromatic plane wave for which transition amplitudes can be calculated including an analytic evaluation <strong>of</strong> the appearing oscillatory integrals [5]. The latter becomes difficult for pulsed plane waves such that this case presents more challenging technical difficulties. While pulsed plane waves have finite extent in time and longitudinal distance they are still <strong>of</strong> infinite transverse size. Introducing a transverse pr<strong>of</strong>ile such as for a Gaussian beam certainly represents a more realistic model but turns out to be difficult to implement in strong-field QED, the main reason being the loss <strong>of</strong> too many conservation laws along with translational invariance. So, for the purposes <strong>of</strong> this talk we will exclusively be dealing with (infinite or pulsed) plane waves. From a relativistic field theory point <strong>of</strong> view, which we have to adopt for a0 > 1, plane electromagnetic waves are <strong>of</strong> a quite peculiar nature. They are described by a wave 4-vector k that is lightlike or null, i.e. k 2 = 0. The electromagnetic field strength, F = (E, B), only depends on the invariant phase, k·x = ωt/c−k·x, where ω is the laser fre-
quency measured in the lab. By Maxwell’s equations, fields are transverse, k ·F = 0, and, most importantly, inherits the null properties from k, E 2 − B 2 = E · B = F 3 = 0. This implies that there is no intrinsic invariant scale characterising an electromagnetic plane wave field. For this reason one needs an external probe momentum, p, to build invariants such that, for instance, a 2 0 ∼ (p · F) 2 [6]. The main effect on such a probe, say an electron, may actually be understood in classical language. Due to the Lorentz force the electron will undergo rapid quiver motion as may be seen by solving for its momentum p(τ) as a function <strong>of</strong> proper time τ. Averaging over the latter the electron acquires a quasi-momentum, q ≡ 〈p(τ)〉 = pin + κ(a 2 0) k, which displays a longitudinal addition to the initial momentum weighted with an a0 dependent prefactor. Squaring this expression and using k 2 = 0 one finds that the electron has become heavier with an effective mass given by m 2 ∗ = m 2 (1 + a 2 0) . (2) This fundamental intensity effect has been predicted long ago [7, 8], but has apparently never been measured. While the appearance <strong>of</strong> the mass shift may be understood quantum mechanically it nevertheless has consequences for the quantum theory. These are best analysed in terms <strong>of</strong> strong field QED. Its ingredients are the usual particle content <strong>of</strong> QED namely photons and electrons <strong>of</strong> arbitrary energy serving e.g. as probes for “quantum diagnostics” when they are coupled to the external laser field. The basic quantum effect is then a dressing <strong>of</strong> the electrons via continuous emission and absorption <strong>of</strong> laser photons. For plane waves this can be taken into account exactly employing the celebrated Volkov solution <strong>of</strong> the Dirac equation [9]. In terms <strong>of</strong> Feynman diagrams the situation is depicted in Fig. 2. Figure 2: The dressed (Volkov) propagator <strong>of</strong> the electron. Transition amplitudes are then constructed in terms <strong>of</strong> Volkov electron lines coupled to probe photons. Laser photons are no longer explicit but hidden in the dressed propagator given by the left-hand side Fig. 2. The main issues to be discussed below will be the dependence <strong>of</strong> these amplitudes on intensity (a0) and finite pulse duration, all in a plane wave context. To give an idea <strong>of</strong> the parameter range involved we present in Fig. 3 a bird’s eye view <strong>of</strong> the probe energy vs. intensity regimes. Conventional high energy physics takes place close to the vertical axis, above the electron pair creation threshold <strong>of</strong> 2mc 2 . In this regime, a first excursion into high-field physics has been made by the SLAC experiment E-144 which utilised 30 GeV photons (obtained via backscattering from the 50 GeV SLAC electron beam) to produce electron positron pairs in collisions with a 10 TW (a0 0.4) laser beam [10]. New facilities such as Vulcan 10 PW or ELI would venture deeply in the high-intensity region (a0 ≫ 1) and may also come close to the pair threshold using Compton backscattering from sufficiently energetic electrons. The latter could in principle be the result <strong>of</strong> laser wake field acceleration. Figure 3: Parameter range <strong>of</strong> strong field QED. A basic example <strong>of</strong> finite pulse duration effects is displayed in Fig. 4 which shows the mass shift, ∆m 2 ≡ m 2 ∗ − m 2 , in a pulse [11] as a function <strong>of</strong> the number N <strong>of</strong> cycles per pulse. There is obviously a “switching on” effect with a sudden increase upon concluding the first cycle after which the infinite plane wave result (2) is approached. It should be emphasised that for current ultra-short pulses <strong>of</strong> a few fs duration the number n is indeed <strong>of</strong> order unity. Figure 4: The mass shift in a pulsed plane wave. STRONG FIELDS: EXAMPLES Nonlinear Compton Scattering (NLC) The Feynman diagrams for NLC are shown in Fig. 5. Expanding the Volkov lines according to Fig. 2 we find that one is essentially summing over all processes <strong>of</strong> the
Page 1 and 2: Proceedings <stron
Page 3: Conference poster
Page 7: Preface The international conferenc
Page 10: Recent progress of
Page 13 and 14: Figure 1: The Pulse Intensity-Durat
Page 15: Figure 3: The attosecond metrology
Page 18 and 19: THE QED EFFECTIVE ACTION In quantum
Page 20 and 21: Figure 2: Turning points in the com
Page 22 and 23: [5] A. Ringwald, “Pair production
Page 26 and 27: form e + nγL → e ′ + γ where
Page 28 and 29: ection(s) associated with the exter
Page 30 and 31: This is listed in Tab.1. The effect
Page 32 and 33: the spectrum of ph
Page 34 and 35: pf f f pi p x2 x1 k ki p pi Figure
Page 36 and 37: STRONG FIELD DYNAMICS IN HEAVY-ION
Page 38 and 39: Possible effects of</strong
Page 40 and 41: Figure 3: Flux tube structure <stro
Page 42 and 43: Abstract Yoctosecond photon pulse g
Page 44 and 45: emsstrahlung or inelastic pair anni
Page 46 and 47: Abstract Fields, Instantons, and Cu
Page 48 and 49: the dispersion relation p0 = Ep −
Page 50 and 51: CRITICAL BEHAVIOR OF CHARMONIUM: QC
Page 52 and 53: different masses m 0 i ̸= mi only
Page 54 and 55: ON THE UNRUH EFFECT ∗ Ralf Schüt
Page 56 and 57: Abstract Can we detect ”Unruh rad
Page 58 and 59: Equipartition Theorem The stochasti
Page 60 and 61: Abstract Quantum fields and static
Page 62: The relation between acceleration a
Page 65 and 66: = γ WISP ; ; ALP HP(mγ ′ > 0) .
Page 67 and 68: Figure 4: Exclusion limit (95% C.L.
Page 69 and 70: Probing extremely light fields via
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Page 73 and 74: Abstract Dynamical view of<
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(a) longitudinal momentum distribut
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Exact solutions of
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Pair production in heat bath Finall
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Table 1: Related ideas in strong fi
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Abstract Non-linear charge transpor
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under the assumption of</st
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Brilliant hardγ-production ande +
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each other. Thus the E field rotate
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ACKNOWLEDGMENTS This work is based
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ϵ is the energy of</strong
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of the sampling eq
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Abstract SCHWINGER LIMIT ATTAINABIL
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To find it we use the integral calc
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cloud with a size of</stron
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A way to quantify the irreversible
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Figure 4: Pair production vs time f
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of the quantum flu
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Phenomena H. Schwarz and H. Hora Ed
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In USA, LLNL has a user’s facilit
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field triggering such phenomena is
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QGP is studied by using the particl
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Fig. (1): Presentation of</
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REFERENCES [1] P.A. Franken, A.E. H
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of electron. When
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splitting, no one has succeeded to
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Abstract WIDE-BAND X-RAY OBSERVATIO
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Radiation from Rotation-Powered Pul
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2 -2 -1 keV (ph cm s keV -1 ) 0.1 0
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Zero temperature case There are sti
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M|, is realized in their case, and
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egime. As analogous to a convention
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With extremely high-peak power lase
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Abstract Flying Mirror as a tool to
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Reflected light intensity (μJ/sr/n
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4-mirror laser stacking cavity for
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CURRENT STATUS OF LFEX LASER AND EX
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which were comparable to those befo
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Abstract X-ray Emission from Magnet
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sometimes exceed the Eddington lumi
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1 0.8 0.6 0.4 0.2 B 2 z E 2 T 0.5 1
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First order quantum correction to t
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dE (1) dt = ¯he4 m 2 12πɛ0p 5 i
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Next, let us consider the origin <s
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Abstract NONCANONICAL LIE PERTURBAT
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with C (2) µ = Γ (2) µ − ˆ L
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log N (PIC particle) When the condi
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Abstract X-RAY GENERATION VIA LASER
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The electron beam is bent to the du
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INVESTIGATING THE ONE-PHOTON ANNIHI
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As a representative characteristics
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the interference terms ⟨ϕIϕh⟩
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P r o g r a m of P
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11:55 lunch & group photo [85] [Rec
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List of Participan
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