All posts by Marek

Electron Acceleration

Recently researchers have successfully accelerated electrons using laser pulses [1]. This achievement is far-reaching and will have immediate practical consequences; including  methods for building less expensive and smaller devices for medicine and materials science applications.  The new method capitalizes on our ability to implement techniques based on commercial near-infrared laser with greater efficiency then any pre-existing technology.

Behind all of this lies a simple idea. A particle’s velocity can be boosted through the interaction between its charge and the electric field component parallel to the particle beam line. Furthermore optimal acceleration conditions, which are experimentally more challenging to meet, dictate that the phase velocity of the accelerating field should always be tuned to the velocity of the relativistic particle.

In this experiment scientist used a micro-fabricated dielectric structure of two gratings (longitudinal cross-section resembles two opposing combs with some space in-between for the electrons to pass through). By preparing the right period for the gratings it was possible to get the diffraction modes of the incident laser pulse to form inside the structure and match the phase resonance conditions.

First results seem to be very promising. This new kind of accelerator offers electron acceleration of 250 MeV/m whereas the standard linear accelerator works at 30 MeV/m. Discoveries utilizing common tools, which promise better solution for practical applications, are always important.

[1] E. A. Peralta et al., Nature, 27 Sept 2013 (10.1038/nature12664)

Jarzynski’s equality

Searching for relations between different physical processes is one of the most successful ways of doing science. Usually these relations are not only surprising but also useful as they offer us a different approach to certain problems. In statistical mechanics such a relation was showed by Christopher Jarzynski [1] who found an equality connecting equilibrium information with non-equilibrium measurements for finite classical systems.

From thermodynamics we know that in the case of quasi-static or, in other words, processes which take an infinitely long time the work done on the system is equal to the difference of Helmholtz free energy of the system. However, for finite time processes some proportion of the work can be dissipated and so in general the total work may surpass the difference of Helmholtz free energy.  Jarzynski’s result shows it still possible to find the value of that difference from finite time measurements which actually makes the whole thing accessible experimentally [2].

To give you some taste how it is done, Jarzynski simply uses the special method of averaging the exponential function of work. This approach provides better weights for different work trajectories to get at the end the mean value of the exponent of dissipated work equaled to one.  It occurs that from Jarzynski’s equality it is easy to derive the fluctuation-dissipation relation as well as the already mentioned inequality between average work and the difference of the system’s free energy.

One interesting question recently asked by researchers was whether there are quantum analogues of this result.  Reported positive answers only prove the general importance of Jarzynski’s equality.

[1] C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).

[2] J. Liphard et al., Science 296, 1832 (2002).

What does it mean to understand in physics?

Every time we learn a new theory which is supposed to explain some physical phenomena we try to understand what is behind its axioms, why certain definitions were introduced and what is the physical meaning of the derived theorems. Let’s think about what it really means to understand and what we want to achieve from our study. Maybe it is fair enough just to be convinced about the significance of the theory without any deeper understanding.

Investigating a problem usually goes for searching for the logical reasoning between facts we find to be a cause of observed effects and using for this physical theories as a framework. To give an example, if we consider the planet movement we expect to take into account the gravitational interaction. Then we are able to foresee their future position but do we really get the underlying physics? The answer is yes; if we only wanted to describe another planetary system, we would succeed in doing so again. However, we cannot be satisfied, at this point we still do not know the interaction mechanism and cannot justify the formula for gravitational force.

With no doubt we should always examine the reasons for which the theory introduces its concepts. It is the best way to get to know all restrictions of the theory and to take a critical look at all made assumptions. On the other hand we will always face the wall of ideas and axioms, which not necessarily have to be intuitive.  The definition of kinetic energy was introduced by classical mechanics and became a part of the everyday language but still it is a purely theoretical notion. So it looks like we are condemned to play the game with known rules, we may even enjoy the game but will never find the explanation of all principles. We have to accept that there is a limit which we will never cross.

Quite often we just accept the validity of formulas and expressions proposed by other researchers. Maybe the reason of this attitude comes from the academic pressure. Having just a taste of the new theory we might be in the position to quickly identify some problems that could be solved within it. Things are fine as long as we remember to take the next step – going into the details of the theory. However, we can also say that using the elaborated model without considering all technical details does not have to indicate we are lazy. We may just want to get the new results based on what has been done by our predecessors.

It is very subjective when we can say, “OK, I’ve understood.” Maybe it is when we are ready to explain certain problems to others or we are just convinced about our knowledge and thanks to it we can predict the results of experiment. Most likely we will never succeed in our attempts to understand the whole nature. Thus the statement  “Still I don’t understand” takes the advantage as it drives our scientific progress.