aa r X i v : . [ a s t r o - ph . H E ] A p r Laboratory gamma-ray pulsar
Andrei Gruzinov
CCPP, Physics Department, New York University, 4 Washington Place, New York, NY 10003
The mechanism by which gamma-ray pulsars shine might be reproducible in a laboratory. Thisclaim is supported by three observations: (i) properly focusing a few PW optical laser gives an elec-tromagnetic field in the so-called Aristotelian regime, when a test electron is radiation-overdamped;(ii) the Goldreich-Julian number density of this electromagnetic field (the number density of ele-mentary charges needed for a nearly full conversion of optical power into gamma-rays) is of orderthe electron number density in a solid; (iii) above about 50PW, the external source of electrons isnot needed – charges will be created by a pair production avalanche.
I. INTRODUCTION
It appears that a gamma-ray pulsar can be created ina laboratory. Real pulsars are efficiently converting thelarge-scale Poynting flux into gamma-rays (up to order-unity efficiency for a weak axisymmetric pulsar, [1] andreferences therein). The laboratory pulsar is expected toefficiently convert optical light into gamma-rays.At the level of estimates, the conditions needed foran efficient Poynting-to-gamma conversion appear to bereproducible in a laboratory. All one needs is (i) Aristotlenumber above one, meaning radiation damping strongerthan inertia, and (ii) the right (namely Goldreich-Julian,[2]) number density of electrons. We discuss these twoconditions in turn.
II. ARISTOTELIAN REGIME
Consider a test electron in the electromagnetic field ofgeneric geometry, | E − B | ∼ | E · B | ∼ F >
0, withcharacteristic length scale λ , and characteristic time scale λ/c . Let us estimate the characteristic Lorentz factor ofthe electron, γ . On the one hand, there exists a maximalpossible γ associated to the full “potential drop” of thefield: γ max ∼ eF λmc , (1)where F ∼ E ∼ B is the characteristic value of electricand magnetic fields, e is the electron charge, m is theelectron mass. On the other hand, there exists a terminalLorentz factor at which the radiation damping balancesthe Lorentz force: γ term ∼ (cid:18) F λ e (cid:19) / . (2)The electron is radiation-overdamped (the field is in theAristotelian regime) if the terminal Lorentz factor isreached in less than the characteristic length scale, thatis if γ max & γ term . (3)Estimating the field from L ∼ cλ F , (4) where L , erg/s, is the laser power, we write the conditionof radiation overdamping asAr ≡ LL e (cid:18) λr e (cid:19) − / & , (5)where we have defined the dimensionless Aristotle num-ber Ar, with L e ≡ mc r e = 8 . × erg/s – the classicalelectron luminosity, and r e ≡ e mc = 2 . × − cm – theclassical electron radius.Assuming that a (split) laser pulse of power L PW × erg/s is focused onto a region of size λ µ × − cm,we get an Aristotle numberAr ∼ . L PW λ − / µ . (6)For λ µ = 0 . L PW >
3, we have Ar > &
1, the work done by thefield goes into emission of curvature photons rather thaninto accelerating electrons. The characteristic photon en-ergy is ǫ ∼ mc α Ar / , (7)where α is the fine structure constant. Pulsars haveAr ≫ III. GOLDREICH-JULIAN NUMBER DENSITY
Each electron emits gamma-rays at a power ∼ eF c ; ifwe want to convert the entire laser pulse into gamma-rays, the number density of electrons n should be n ∼ Lλ eF c ∼ cλ F λ eF c ∼ Feλ . (8)In pulsar physics, the last expression is known as theGoldreich-Julian density – this is the number density ofelementary charges needed to noticeably alter the exter-nal field ∼ F . Numerically, n GJ ∼ . × L / λ − µ cm − (9)is of order the number density in a solid.We also note that above about 50PW, the pairavalanche will (over) produce the necessary charge den-sity starting from a single seed charge as described in [3]:a seed charge emits gamma rays; gamma-rays pair pro-duce in external magnetic field; pairs then emit gamma-rays, etc. IV. CONCLUSION
When powerful lasers are properly focused on a targetor even on vacuum, an efficient optical to gamma-ray conversion should occur, enabled by the same mechanismby which the gamma-ray pulsars shine. [1] A. Gruzinov, arXiv:1402.1520 (2014)[2] P. Goldreich, W. H. Julian, Astrophys. J. , 869 (1969)[3] M. A. Ruderman, P. G. Sutherland, Astrophys. J.196