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In [[accelerator physics]], the term '''acceleration voltage''' means the effective [[voltage]] surpassed by a charged [[particle]] along a defined straight line. If not specified further, the term is likely to refer to the ''longitudinal effective acceleration voltage'' <math>V_\parallel</math>.
If you are doing home improvement projects, you may be wondering if you can save money by taking on some of them yourself. The answer is yes, but you will want to weigh the options and make the best choices. This article will give you tips for doing it yourself and deciding when to call in the pros.<br><br>Be on the lookout for any carpet installation sales or promotions at your local home improvement retailers. In order to gain customers, they will install carpet for cheap prices. This makes for a perfect opportunity to get new carpet into the house, because labor itself, rather than the carpet, is often the most expensive aspect of the process.<br><br>Texturing walls using drywall mud can add visual interest and cover up many blemishes. It is not hard to do. You only need to apply the drywall mud to the wall and then press to add an interesting texture with a sponge, brush or crumpled up paper bag.<br><br>You can add some flare to your book case by putting some wall paper there. Choose a fun and original wallpaper design. Paste the wallpaper onto the inside of the bookcase to give your favorite books a fashionable backdrop. Your new, distinctive bookcase will look better, and it can even dictate the decor of the rest of the room<br><br>Texturing walls using drywall mud can add visual interest and cover up many blemishes. Adding texture is simple. Trowel drywall mud and then use a sponge, stiff-bristled brush, or just a wadded up trash bag to add texture.<br><br>Create a plan before starting a landscaping project to ensure that fits with the look of your home. A new garden or outside dining area that goes well with your home's style will improve the entire look of your property, but things that clash will offer the appearance of insufficient planning and end up looking outright unattractive.<br><br>Whenever you are working on a home improvement project that involves bricks, it is wise to purchase extras. It is next to impossible to get a good color match if there are needed repairs or additions in the future. Brick styles change often. Keeping a small supply of surplus bricks, of the identical style as the ones originally used, will make it much easier to match for future projects.<br><br>Be sure to include a window or other ventilation mechanism with any improvements to your bathroom. Mold can grow quickly in the moisture left behind by daily showering. Even if you keep repainting your bathroom walls, it still won't sufficiently kill off the mold. Prevent mold from growing in the first place. Reduce the humidity in the space with ventilation or a window.<br><br>Increasing living area makes any home more functional. Perhaps a playroom would be a good idea or even an exercise room. This will increase the value of your home, and it will improve your living environment. Save up for something like this, though, so you don't get in over your head.<br><br>A front door that makes a great first impression on potential buyers can increase your homes value by up to 10 percent. An existing door can be easily enhanced with new locks and knobs.<br><br>An excellent idea is to put in a fence around your backyard because this can achieve many different purposes in your home renovation. You will be protected from stray animals in the neighborhood. A fence can also keep a dog from leaving the yard. A fence is something that all homes need to look complete.<br><br>Make sure you get the right measurements for blinds before purchasing or installing them. Without measuring properly, you may have trouble installing the blinds correctly. There are many different sizes for blinds and some are made to be installed on the interior frame of the window and some on the outside of the frame.<br><br>Now that you're better quipped with useful tips, you should now be ready to work and succeed on future projects.  If you loved this informative article and you wish to receive details concerning kitchen home improvement ([http://www.homeimprovementdaily.com get more info]) i implore you to visit our own web site. Make your renovation and home improvement ideas a reality through the use of your creativity and keep disasters at bay with the aid of the provided tips.
 
The acceleration voltage is an important quantity for the design of [[microwave cavity|microwave cavities]] for [[particle accelerator]]s. See also [[shunt impedance]].
 
For the special case of an electrostatic field that is surpassed by a particle, the acceleration voltage is directly given by integrating the electric field along its path. The following considerations are generalized for time-dependent fields.
 
{{ambox
|image = [[File:Info.svg|30px]]
|text = There are several '''variant definitions''' for the terms [[shunt impedance]] and [[acceleration voltage]] relating to transit time dependence.<ref name="lee">{{cite book | url=http://books.google.com/?id=VTc8Sdld5S8C&printsec=frontcover&dq=Accelerator+physics#v=onepage&q=Accelerator%20physics&f=false | title=Accelerator physics | publisher=[[World Scientific]] | date=2004 | edition = 2nd | last1 = Lee | first1 = Shyh-Yuan | isbn = 978-981-256-200-5 }}
</ref><ref name="wangler">{{cite book
|title= RF Linear Accelerators
|last1= Wangler |first1= Thomas |authorlink1=
|coauthors=
|editor1-last= |editor1-first= | editor1-link=
|edition= 2nd
|date= 2008
|publisher= [[Wiley-VCH]]
|location=
|isbn= 978-3-527-62343-3
|pages=
|url= http://books.google.de/books?id=OJdgVI-UrikC&printsec=frontcover
}} (slightly different notation)</ref> To clear this point, this page differentiates between ''effective'' (including transit time factor) and ''time-independent'' quantities.
}}
 
== Longitudinal voltage ==
 
The longitudinal '''effective acceleration voltage''' is given by the kinetic energy gain experienced by a particle with velocity <math>\beta c</math> along a defined straight path (path integral of the longitudinal Lorentz forces) divided by its charge,<ref name="wangler" />
 
<math> V_\parallel(\beta) = \frac 1 q \vec e_s \cdot \int \vec F_L(s,t) \,\mathrm{d}s = \frac 1 q \vec e_s \cdot \int \vec F_L(s, t = \frac{s}{\beta c}) \,\mathrm d s </math>.
 
For resonant structures, e.g. [[Superconducting Radio Frequency|SRF cavities]], this may be expressed as a [[Fourier transform|Fourier integral]], because the fields <math>\vec E,\vec B</math>, and the resulting [[Lorentz force]] <math>\vec F_L</math>, are proportional to <math>\exp(i \omega t)</math> ([[eigenmode]]s)
 
<math> V_\parallel(\beta) = \frac{1}{q} \vec e_s \cdot \int \vec F_L(s) \exp\left(i \frac{\omega}{\beta c} s\right)\,\mathrm d s = \frac{1}{q} \vec e_s \cdot \int \vec F_L(s) \exp\left(i k_\beta s\right)\,\mathrm d s </math> with <math>k_\beta = \frac{\omega}{\beta c} </math>
 
Since the particles [[kinetic energy]] can only be changed by electric fields, this reduces to
 
<math> V_\parallel(\beta) = \int E_s(s) \exp\left(i k_\beta s\right)\,\mathrm d s </math>
 
=== Particle Phase considerations ===
 
Note that by the given definition, <math>V_\parallel</math> is a [[complex number|complex quantity]]. This is advantageous, since the relative phase between particle and the experienced field was fixed in the previous considerations (the particle travelling through <math>s=0</math> experienced maximum electric force).
 
To account for this [[Degrees of freedom (physics and chemistry)|degree of freedom]], an additional phase factor <math>\phi</math> is included in the [[eigenmode]] field definition
 
<math> E_s(s,t) = E_s(s) \; \exp\left(i \omega t + i \phi \right) </math>
 
which leads to a modified expression
 
<math> V_\parallel(\beta) = e^{i \phi} \int E_s(s) \exp\left(i k_\beta s\right)\,\mathrm d s </math>
 
for the voltage. In comparison to the former expression, only a phase factor with unit length occurs. Thus, the ''absolute value'' of the complex quantity <math> | V_\parallel(\beta) | </math> is independent of the particle-to-eigenmode phase <math>\phi</math>. It represents the maximum achievable voltage that is experienced by a particle with optimal phase to the applied field, and is the relevant physical quantity.
 
=== Transit time factor ===
 
A quantity named ''transit time factor''<ref name="wangler" />
 
<math>T(\beta) = \frac{|V_\parallel|}{V_0} </math>
 
is often defined which relates the effective acceleration voltage <math>V_\parallel(\beta)</math> to the '''time-independent acceleration voltage'''
 
<math>V_0 = \int E(s)\,\mathrm d s</math>.
 
In this notation, the effective acceleration voltage <math>|V_\parallel|</math> is often expressed as <math>V_0 T</math>.
 
== Transverse voltage ==
 
In symbolic analogy to the longitudinal voltage, one can define effective voltages in two orthogonal directions <math>x,y</math> that are transversal to the particle trajectory
 
<math> V_{x,y} = \frac{1}{q} \vec e_{x,y} \cdot \int \vec F_L(s) \exp\left(i k_\beta s\right)\,\mathrm d s </math>
 
which describe the integrated forces that deflect the particle from its design path. Since the modes that deflect particles may have arbitrary polarizations, the ''transverse effective voltage'' may be defined using polar notation by
 
<math> V_\perp^2(\beta) = V_x^2 + V_y^2, \quad \alpha = \arctan \frac{\tilde V_y}{\tilde V_x} </math>
 
with the ''polarization angle'' <math>\alpha</math>
The tilde-marked variables are not absolute values, as one might expect, but can have positive or negative sign, to enable a range <math>[-\pi/2,+\pi/2]</math> for <math>\alpha</math>. For example, if <math>\tilde V_x = | V_x |</math> is defined, then <math>\tilde V_y = V_y \cdot \exp(-i \arg V_x) \in \mathbb R</math> must hold.
 
Note that this transverse voltage does '''not''' necessarily relate to a real change in the particles energy, since magnetic fields are also able to deflect particles. Also, this is an approximation for small-angle deflection of the particle, where the particles trajectory through the field can still be approximated by a straight line.
 
== References ==
{{Reflist}}
 
[[Category:Accelerator physics]]

Latest revision as of 18:47, 28 October 2014

If you are doing home improvement projects, you may be wondering if you can save money by taking on some of them yourself. The answer is yes, but you will want to weigh the options and make the best choices. This article will give you tips for doing it yourself and deciding when to call in the pros.

Be on the lookout for any carpet installation sales or promotions at your local home improvement retailers. In order to gain customers, they will install carpet for cheap prices. This makes for a perfect opportunity to get new carpet into the house, because labor itself, rather than the carpet, is often the most expensive aspect of the process.

Texturing walls using drywall mud can add visual interest and cover up many blemishes. It is not hard to do. You only need to apply the drywall mud to the wall and then press to add an interesting texture with a sponge, brush or crumpled up paper bag.

You can add some flare to your book case by putting some wall paper there. Choose a fun and original wallpaper design. Paste the wallpaper onto the inside of the bookcase to give your favorite books a fashionable backdrop. Your new, distinctive bookcase will look better, and it can even dictate the decor of the rest of the room

Texturing walls using drywall mud can add visual interest and cover up many blemishes. Adding texture is simple. Trowel drywall mud and then use a sponge, stiff-bristled brush, or just a wadded up trash bag to add texture.

Create a plan before starting a landscaping project to ensure that fits with the look of your home. A new garden or outside dining area that goes well with your home's style will improve the entire look of your property, but things that clash will offer the appearance of insufficient planning and end up looking outright unattractive.

Whenever you are working on a home improvement project that involves bricks, it is wise to purchase extras. It is next to impossible to get a good color match if there are needed repairs or additions in the future. Brick styles change often. Keeping a small supply of surplus bricks, of the identical style as the ones originally used, will make it much easier to match for future projects.

Be sure to include a window or other ventilation mechanism with any improvements to your bathroom. Mold can grow quickly in the moisture left behind by daily showering. Even if you keep repainting your bathroom walls, it still won't sufficiently kill off the mold. Prevent mold from growing in the first place. Reduce the humidity in the space with ventilation or a window.

Increasing living area makes any home more functional. Perhaps a playroom would be a good idea or even an exercise room. This will increase the value of your home, and it will improve your living environment. Save up for something like this, though, so you don't get in over your head.

A front door that makes a great first impression on potential buyers can increase your homes value by up to 10 percent. An existing door can be easily enhanced with new locks and knobs.

An excellent idea is to put in a fence around your backyard because this can achieve many different purposes in your home renovation. You will be protected from stray animals in the neighborhood. A fence can also keep a dog from leaving the yard. A fence is something that all homes need to look complete.

Make sure you get the right measurements for blinds before purchasing or installing them. Without measuring properly, you may have trouble installing the blinds correctly. There are many different sizes for blinds and some are made to be installed on the interior frame of the window and some on the outside of the frame.

Now that you're better quipped with useful tips, you should now be ready to work and succeed on future projects. If you loved this informative article and you wish to receive details concerning kitchen home improvement (get more info) i implore you to visit our own web site. Make your renovation and home improvement ideas a reality through the use of your creativity and keep disasters at bay with the aid of the provided tips.

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